REVIEW 2 major objections 6 minor 299 references
Stability for boundary actions of cocompact lattices in Euclidean buildings
T0 review · 2 major / 6 minor · reviewed 2026-08-02 · deepseek-v4-flash
Pith's one-line read The induced action of a cocompact lattice on every flag space of a locally compact Euclidean building is topologically stable: every sufficiently small perturbation is semi-conjugate to the original action.
desk verdict A genuinely new and likely correct C0 stability theorem for boundary actions of cocompact lattices in higher-rank Euclidean buildings, with one small but real gap in Corollary 3.16 that should be patchable. read the letter →
The pith
A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.
The reading
What carries the argument
The proof rests on a general stability criterion built from finitary point coders: finite directed graphs whose vertices are open subsets of the flag space and whose edges are labeled by group elements, so that an infinite path yields a nested intersection coding a point. Two such coders, related by an interpolation property, turn coding data into a semi-conjugacy. To build the coders, the paper proves a quantitative expansivity estimate: for each flag z, some group element moving the basepoint far out along a Weyl cone over z contracts nearby flags by a factor E in an ultrametric visual metric. A higher-rank Morse lemma, quoted as a black box, guarantees that uniformly regular quasi-geodesi
What would settle it
Look for a locally compact Euclidean building and a compact set Θ inside the open star of τmod for which some Θ-regular quasi-geodesic sequence does not lie in any bounded neighborhood of a single Weyl cone V(x0,st(τ)) over a unique τmod-flag. Finding one such sequence would refute the quoted higher-rank Morse lemma and remove the mechanism that converts coding data into regular quasi-geodesics, so the paper's argument would no longer go through.
Extended reading notes
Core claim
The central claim is that the action ρ0 of a cocompact lattice Γ on a flag boundary M of a locally compact Euclidean building is topologically stable. Concretely, there is a neighborhood of ρ0 in the space of all homomorphisms Γ→Homeo(M) such that every action ρ in that neighborhood is semi-conjugate to ρ0: a continuous surjection M→M intertwines ρ with ρ0. Because M is a Cantor set for each choice of flag type, semi-conjugacy is the natural C0 equivalence; the paper shows in Section 7 that it cannot generally be improved to conjugacy, even though bi-Lipschitz perturbations would admit such an upgrade. A direct corollary is that for any semisimple p-adic Lie group G, any parabolic subgroup Q
Load-bearing premise
The load-bearing assumption is the higher-rank Morse lemma: uniformly regular quasi-geodesic sequences in a Euclidean building stay within a bounded distance of a Weyl cone over a unique boundary flag; if that statement failed, the coding construction and the interpolation property would collapse.
Editorial extensions
If this is right
- Every cocompact lattice in a semisimple p-adic Lie group acts topologically stably on G/Q for every parabolic subgroup Q.
- Semi-conjugacy is optimal in general: the paper constructs arbitrarily small perturbations of a rank-two p-adic flag action that are not conjugate to the original action, only semi-conjugate.
- If attention is restricted to bi-Lipschitz perturbations, the semi-conjugacy upgrades to a genuine conjugacy.
- The coding criterion is a general device: any action admitting two stable proto-coders satisfying contraction, separation, and interpolation is topologically stable, independent of the building geometry.
Reading between the lines
- A natural testable extension is to apply the same expansivity-plus-Morse-lemma combination to other CAT(0) spaces with a regular quasi-geodesic theory, such as higher-rank symmetric spaces, where no C0 stability result is currently known for nonuniform lattices.
- The blowup construction suggests that topological stability, rather than conjugacy, is the correct expected rigidity in the totally disconnected setting; this may guide targeted results in the p-adic analogue of the general program on classifying actions of large groups.
- Because the interpolation property is the only place where the higher-rank Morse lemma enters, one could test the machinery by replacing that lemma with a synthetic 'straightness' axiom and checking which groups acting on which flag boundaries satisfy it.
- The paper's rank-two counterexample may generalize to all ranks at least two, indicating that the C0 stability theorem is sharp in a way that would not be visible from smooth or bi-Lipschitz rigidity alone.
Editorial analysis
A structured set of objections, weighed in public.
Referee Report
Summary. The paper proves Theorem 1.1: for a locally compact Euclidean building X and a group Γ acting properly and cocompactly by isometries on X, the induced action on the space M of τmod-flags in the visual boundary is topologically stable: every sufficiently small perturbation of ρ0 in Hom(Γ, Homeo(M)) is semi-conjugate to ρ0. The proof is modular. Section 2 develops an automata-theoretic stability criterion (Theorem 2.12) in terms of two proto-coders and four conditions (P1)–(P4). Section 4 proves a quantitative expansivity/contraction estimate (Theorem 4.1) for the action on flag boundaries. Section 5 constructs proto-coders from cocompact building actions, using the Kapovich–Leeb–Porti higher-rank Morse lemma (quoted as Theorem 3.15) to pass between regular quasi-geodesics and codings. Section 6 establishes an interpolation property (Proposition 6.1) and assembles the proof of Theorem 1.1. Section 7 gives an example showing that semi-conjugacy cannot in general be upgraded to conjugacy. Corollary 1.3 applies the theorem to parabolic quotients G/Q for semisimple p-adic Lie groups.
Significance. If correct, this is a substantial advance: it extends C0 boundary stability beyond hyperbolic/rank-one and real higher-rank settings to Euclidean buildings and totally disconnected flag spaces, where no smooth structure is available. The paper is careful with quantified constants, makes the logical architecture transparent, and includes a counterexample showing the optimality of semi-conjugacy. Its main strengths are the clean separation of the stability criterion from the geometric construction, the explicit use of the higher-rank Morse lemma, and the detailed verification of the coding properties. The principal caveat is the heavy reliance on the quoted Morse lemma and one under-justified step in the proof of Corollary 3.16; with that repaired, the result is significant and publishable.
major comments (2)
- [Section 3.8, Corollary 3.16] The proof of Corollary 3.16 applies Theorem 3.15 to each tail and then asserts that uniqueness of the Morse-lemma flag gives τ_n = τ_0. As stated, Theorem 3.15 fixes the basepoint as the first term of the sequence and gives a constant D depending only on Θ,K,A; a tail with basepoint x_n need not satisfy the same D-neighborhood condition for τ_0, so uniqueness for the tail does not, by itself, identify its flag with τ_0. This identification is load-bearing: Corollary 3.16 is used in Proposition 5.11, Proposition 5.15, and the interpolation argument in Proposition 6.1, and hence for property (P4) in the proof of Theorem 1.1. Please fill this step, for example using Lemma 3.8/separated stars, or quote explicitly a stronger tail-independence statement from [KLP18].
- [Sections 5–6 (proof of Theorem 1.1)] The coding construction is contingent on the exact uniformity of the quoted higher-rank Morse lemma ([KLP18, Theorem 1.3], stated here as Theorem 3.15). Propositions 5.11, 5.15, and 6.1 each require that the constant D depend only on Θ,K,A, and that the associated flag be unique for the whole sequence and its tails. The manuscript does not prove this uniformity and does not isolate the precise statement it needs from [KLP18]. This is an external-input risk rather than an internal inconsistency, but it is load-bearing: if the required uniformity fails, the coding construction and (P4) collapse. Please add an explicit statement of the exact uniformity hypothesis used, with a precise reference to the corresponding statement in [KLP18].
minor comments (6)
- [Section 2] Many cross-references are mislabeled: Definition 2.3 is cited as Theorem 2.3, Lemma 2.5 as Theorem 2.5, Remark 2.7 as Theorem 2.7, Definition 2.9 as Theorem 2.9, Lemma 2.11 as Theorem 2.11, Lemma 2.14 as Theorem 2.14, Corollary 2.15 as Theorem 2.15, and Lemma 2.16 as Theorem 2.16. Please correct.
- [Lemma 2.18 proof] The displayed line "Φ(ϕ(ρ(γ)p))⊂W(z)" appears to be a typo. The intended argument seems to be that ρ(γ)p ∈ ρ(γ)Φ(ϕ(p)) = Φ(ρ0(γ)ϕ(p)) ⊂ W(z). Please rephrase.
- [Lemma 5.10 proof] Near the end of the proof, d_X(u,v) is used for points u,v in the boundary flag space M; this should be d_o (or another metric on M), not the metric on X.
- [Theorem 4.1 proof] The proof begins by taking x,y∈B(γ^{-1}τ, ϵ0), but the statement uses ϵ. Unify the notation and make the dependence of ϵ on the constants explicit.
- [Section 6, proof of Proposition 6.1] In the inductive construction of (w_k), the line "y_n ∈ V(w_{n_k}, st_{Θ'}(τ))" should read "y_n ∈ V(w_k, st_{Θ'}(τ))". Also, references to "Theorem 5.5" and "Theorem 5.2" should be to "Remark 5.5" and "Proposition 5.2" respectively.
- [Corollary 1.3] The assertion that every lattice in a semisimple p-adic Lie group is uniform is used without a reference or proof. If this is standard, please supply a citation; if it is not always true, the statement of the corollary needs adjustment.
Circularity Check
No circularity: the coding construction is an independent geometric argument; self-cited coder lemmas are published and the KLP Morse lemma is an external input, not a restatement of the theorem.
full rationale
I walked the derivation chain. Section 2 states and proves a general automata-theoretic stability criterion (Theorem 2.12); the only imported ingredient is Lemma 2.5, quoted from [MMW24, Lemma A.3]. That lemma is a published, parameter-free statement about contracting point coders whose hypotheses (finite F, ρ-contracting coders) do not include the building action or topological stability, so under rule 4 the self-citation is genuine independent evidence rather than a circular load. Sections 3–5 construct the proto-coders from the geometry of the building, using the higher-rank Morse lemma of Kapovich–Leeb–Porti (Theorem 3.15, quoted from [KLP18, Theorem 1.3]) as the external mechanism converting Θ-regular quasi-geodesics into unique τmod-flags and back; this is an external-input dependency, not a circular reduction. The paper explicitly worries about constant-ordering in Remark 5.5 and the proof of Proposition 5.11, Lemma 5.17, and Proposition 5.15 indeed choose L before ϵ, with ϵ depending on L but never L on ϵ, so no hidden self-definitional dependence appears. Section 6 proves the interpolation property using [KLP18, Lemma 3.11] and the nesting lemma, and then feeds it into condition (P4); no fitted parameter is renamed as a prediction and no equation reduces to its own input by construction. The proof of Corollary 3.16 contains a step where the equality τ_n = τ is asserted from the uniqueness part of Theorem 3.15; this is a potential proof gap or external-uniformity risk, not a circularity, and does not change the verdict. The central claim is conditional on KLP18's Morse lemma and on MMW24's Lemma A.3, but those are external published results, so the appropriate finding is no circularity.
Assumptions & free parameters
assumptions (5)
- domain assumption Higher-rank Morse lemma for Euclidean buildings ([KLP18, Thm 1.3]; quoted as Thm 3.15): every Θ-regular (K,A)-quasi-geodesic is uniformly close to a Weyl cone over a unique τmod-flag.
- domain assumption A locally compact Euclidean building all of whose irreducible factors have rank at least 3 is the Bruhat–Tits building of a semisimple p-adic Lie group (Tits [Tit74]).
- standard math CAT(0) and building axioms: visual boundary, spherical building structure, type map θ, logarithm maps, nesting and separated stars (lemmas from [KL97] and [KLP18] invoked throughout).
- standard math Milnor–Schvarcz lemma: a proper cocompact action of Γ on X makes the orbit map a quasi-isometry between Γ and X.
- domain assumption The ultrametric d_o on the flag space M is well-defined and compatible with the cone topology.
Cite this review
Pith. "Pith review of Stability for boundary actions of cocompact lattices in Euclidean buildings." pith.science (2026). https://pith.science/paper/S4DPJHTJ
@misc{pith2026260714668,
author = {Pith},
title = {Pith review of: Stability for boundary actions of cocompact lattices in Euclidean buildings},
year = {2026},
howpublished = {\url{https://pith.science/paper/S4DPJHTJ}},
note = {Machine review of arXiv:2607.14668}
}
abstract
When $X$ is a locally compact Euclidean building, the isometry group of $X$ acts by homeomorphisms on the space of $k$-simplices in the visual boundary of $X$. We consider perturbations of these actions for discrete groups of isometries acting with compact quotient on $X$, showing that all small enough perturbations are semi-conjugate to the original action. This proves in particular that, when $Q$ is any parabolic subgroup in a semisimple $p$-adic Lie group $G$, the induced action of a cocompact lattice in $G$ has a topologically stable action on $G/Q$.
Figures
Figures from the paper (4 more)
Reference graph
Works this paper leans on
-
[1]
Margulis, G. A. , TITLE =. Dokl. Akad. Nauk SSSR , FJOURNAL =. 1969 , NUMBER =
1969
-
[2]
Pecastaing, Vincent , TITLE =. Math. Ann. , FJOURNAL =. 2024 , NUMBER =. doi:10.1007/s00208-022-02528-z , URL =
-
[3]
Pecastaing, Vincent , TITLE =. Geom. Funct. Anal. , FJOURNAL =. 2020 , NUMBER =. doi:10.1007/s00039-020-00537-1 , URL =
-
[4]
Boundary actions by higher-rank lattices: Classification and embedding in low dimensions, local rigidity, smooth factors. arXiv e-prints , keywords =. doi:10.48550/arXiv.2405.16202 , archivePrefix =. 2405.16202 , primaryClass =
-
[5]
Brown, Aaron and Rodriguez Hertz, Federico and Wang, Zhiren , TITLE =. Ann. of Math. (2) , FJOURNAL =. 2022 , NUMBER =. doi:10.4007/annals.2022.196.3.1 , URL =
-
[6]
Entropy-rigidity of locally symmetric spaces of negative curvature , JOURNAL =
Hamenst\". Entropy-rigidity of locally symmetric spaces of negative curvature , JOURNAL =. 1990 , NUMBER =. doi:10.2307/1971507 , URL =
-
[7]
Fayad, Bassam and Khanin, Kostantin , TITLE =. Ann. of Math. (2) , FJOURNAL =. 2009 , NUMBER =. doi:10.4007/annals.2009.170.961 , URL =
-
[8]
Herman, Michael-Robert , TITLE =. Inst. Hautes \'. 1979 , PAGES =
1979
Show all 299 references
-
[9]
Leeb, Bernhard , TITLE =. Invent. Math. , FJOURNAL =. 1995 , NUMBER =. doi:10.1007/BF01231445 , URL =
1995 doi
-
[10]
and Leeb, B
Kapovich, M. and Leeb, B. , TITLE =. Geom. Funct. Anal. , FJOURNAL =. 1998 , NUMBER =. doi:10.1007/s000390050076 , URL =
1998 doi
-
[11]
Kleiner, Bruce and Lang, Urs , TITLE =. Invent. Math. , FJOURNAL =. 2020 , NUMBER =. doi:10.1007/s00222-020-00955-w , URL =
2020 doi
-
[12]
and Minsky, Yair N
Behrstock, Jason A. and Minsky, Yair N. , TITLE =. J. Lond. Math. Soc. (2) , FJOURNAL =. 2011 , NUMBER =. doi:10.1112/jlms/jdr027 , URL =
2011 doi
-
[13]
Local limit theorem for symmetric random walks in
Gou\". Local limit theorem for symmetric random walks in. J. Amer. Math. Soc. , FJOURNAL =. 2014 , NUMBER =. doi:10.1090/S0894-0347-2014-00788-8 , URL =
2014 doi
-
[14]
2002 , PAGES =
Valette, Alain , TITLE =. 2002 , PAGES =. doi:10.1007/978-3-0348-8187-6 , URL =
2002 doi
-
[15]
Lafforgue, Vincent , TITLE =. C. R. Acad. Sci. Paris S\'. 1998 , NUMBER =. doi:10.1016/S0764-4442(99)80019-6 , URL =
1998 doi
-
[16]
Connes, Alain and Moscovici, Henri , TITLE =. C. R. Acad. Sci. Paris S\'. 1988 , NUMBER =
1988
-
[17]
and Schroeder, Viktor , TITLE =
Anderson, Michael T. and Schroeder, Viktor , TITLE =. Invent. Math. , FJOURNAL =. 1986 , NUMBER =. doi:10.1007/BF01389092 , URL =
1986 doi
-
[18]
Connell, Christopher and Farb, Benson , TITLE =. Comm. Anal. Geom. , FJOURNAL =. 2003 , NUMBER =. doi:10.4310/CAG.2003.v11.n5.a7 , URL =
2003 doi
-
[19]
Forum Math
Liu, Beibei and Wang, Shi , TITLE =. Forum Math. Sigma , FJOURNAL =. 2023 , PAGES =. doi:10.1017/fms.2023.73 , URL =
2023 doi
-
[20]
2022 , eprint=
Polynomial effective density in quotients of H^3 and H^2 H^2 , author=. 2022 , eprint=
2022
-
[21]
Bader, Uri and Fisher, David and Miller, Nicholas and Stover, Matthew , TITLE =. Invent. Math. , FJOURNAL =. 2023 , NUMBER =. doi:10.1007/s00222-023-01186-5 , URL =
2023 doi
-
[22]
Finiteness of maximal geodesic submanifolds in hyperbolic hybrids , JOURNAL =
Fisher, David and Lafont, Jean-Fran. Finiteness of maximal geodesic submanifolds in hyperbolic hybrids , JOURNAL =. 2021 , NUMBER =. doi:10.4171/jems/1077 , URL =
2021 doi
-
[23]
Bader, Uri and Fisher, David and Miller, Nicholas and Stover, Matthew , TITLE =. Ann. of Math. (2) , FJOURNAL =. 2021 , NUMBER =. doi:10.4007/annals.2021.193.3.4 , URL =
2021 doi
-
[24]
Pesin, Ja. B. , TITLE =. Izv. Akad. Nauk SSSR Ser. Mat. , FJOURNAL =. 1977 , NUMBER =
1977
-
[25]
and Ivanov, S
Burago, D. and Ivanov, S. , TITLE =. Geom. Funct. Anal. , FJOURNAL =. 1994 , NUMBER =. doi:10.1007/BF01896241 , URL =
1994 doi
-
[26]
Time-preserving conjugacies of geodesic flows , JOURNAL =
Hamenst\". Time-preserving conjugacies of geodesic flows , JOURNAL =. 1992 , NUMBER =. doi:10.1017/S0143385700006581 , URL =
1992 doi
-
[27]
Guillarmou, Colin and Lefeuvre, Thibault , TITLE =. Ann. of Math. (2) , FJOURNAL =. 2019 , NUMBER =. doi:10.4007/annals.2019.190.1.6 , URL =
2019 doi
-
[28]
, TITLE =
Croke, Christopher B. , TITLE =. Geometric methods in inverse problems and. 2004 , ISBN =. doi:10.1007/978-1-4684-9375-7\_4 , URL =
2004 doi
-
[29]
2023 , eprint=
Boundary actions of lattices and C^0 local semi-rigidity , author=. 2023 , eprint=
2023
-
[30]
, TITLE =
Kanai, M. , TITLE =. Geom. Funct. Anal. , FJOURNAL =. 1996 , NUMBER =. doi:10.1007/BF02246995 , URL =
1996 doi
-
[31]
Ralf Spatzier and Kurt Vinhage , title=. J. Amer. Math. Soc. , Fjournal =. 2023 , Pages =
2023
-
[32]
Group actions in ergodic theory, geometry, and topology---selected papers , PAGES =
Fisher, David , TITLE =. Group actions in ergodic theory, geometry, and topology---selected papers , PAGES =. 2020 , ISBN =
2020
-
[33]
Large groups actions on manifolds , BOOKTITLE =
Labourie, Fran. Large groups actions on manifolds , BOOKTITLE =. Doc. Math. , FJOURNAL =. 1998 , NUMBER =
1998
-
[34]
Franks, John and Handel, Michael , TITLE =. Geom. Topol. , FJOURNAL =. 2003 , PAGES =. doi:10.2140/gt.2003.7.757 , URL =
2003 doi
-
[35]
Polterovich, Leonid , TITLE =. Invent. Math. , FJOURNAL =. 2002 , NUMBER =. doi:10.1007/s00222-002-0251-x , URL =
2002 doi
-
[36]
, TITLE =
Zimmer, Robert J. , TITLE =. Inst. Hautes \'. 1984 , PAGES =
1984
-
[37]
, TITLE =
Zimmer, Robert J. , TITLE =. Bull. Amer. Math. Soc. (N.S.) , FJOURNAL =. 1983 , NUMBER =. doi:10.1090/S0273-0979-1983-15093-0 , URL =
1983 doi
-
[38]
Topology , FJOURNAL =
Farb, Benson and Shalen, Peter , TITLE =. Topology , FJOURNAL =. 2000 , NUMBER =. doi:10.1016/S0040-9383(99)00020-8 , URL =
2000 doi
-
[39]
Brown, Aaron and Rodriguez Hertz, Federico and Wang, Zhiren , TITLE =. Ann. of Math. (2) , FJOURNAL =. 2017 , NUMBER =. doi:10.4007/annals.2017.186.3.3 , URL =
2017 doi
-
[40]
Farb, Benson and Shalen, Peter , TITLE =. Invent. Math. , FJOURNAL =. 1999 , NUMBER =. doi:10.1007/s002220050286 , URL =
1999 doi
-
[41]
Witte, Dave , TITLE =. Proc. Amer. Math. Soc. , FJOURNAL =. 1994 , NUMBER =. doi:10.2307/2161021 , URL =
1994 doi
-
[42]
Geometry, rigidity, and group actions , SERIES =
Weinberger, Shmuel , TITLE =. Geometry, rigidity, and group actions , SERIES =. 2011 , MRCLASS =
2011
-
[43]
Actions de r\'
Ghys, \'. Actions de r\'. Invent. Math. , FJOURNAL =. 1999 , NUMBER =. doi:10.1007/s002220050329 , URL =
1999 doi
-
[44]
Actions de groupes de
Navas, Andr\'. Actions de groupes de. Ann. Sci. \'. 2002 , NUMBER =. doi:10.1016/S0012-9593(02)01107-2 , URL =
2002 doi
- [45]
-
[46]
and Monod, N
Burger, M. and Monod, N. , TITLE =. J. Eur. Math. Soc. (JEMS) , FJOURNAL =. 1999 , NUMBER =. doi:10.1007/s100970050007 , URL =
1999 doi
- [47]
-
[48]
and Lewis, J
Katok, A. and Lewis, J. , TITLE =. Israel J. Math. , FJOURNAL =. 1996 , PAGES =. doi:10.1007/BF02761106 , URL =
1996 doi
-
[49]
, TITLE =
Kuroki, S. , TITLE =. Fundam. Prikl. Mat. , FJOURNAL =. 2005 , NUMBER =. doi:10.1007/s10958-007-0365-1 , URL =
2005 doi
-
[50]
Uchida, Fuichi , TITLE =. Publ. Res. Inst. Math. Sci. , FJOURNAL =. 1985 , NUMBER =. doi:10.2977/prims/1195179632 , URL =
1985
-
[51]
Calabi, Eugenio and Vesentini, Edoardo , TITLE =. Ann. of Math. (2) , FJOURNAL =. 1960 , PAGES =. doi:10.2307/1969939 , URL =
1960 doi
-
[52]
and Spatzier, Ralf J
Goetze, Edward R. and Spatzier, Ralf J. , TITLE =. Duke Math. J. , FJOURNAL =. 1997 , NUMBER =. doi:10.1215/S0012-7094-97-08801-3 , URL =
1997 doi
-
[53]
Buyalo, S. V. and Kobelski. Geometrization of graph-manifolds. Algebra i Analiz , FJOURNAL =. 1995 , NUMBER =
1995
-
[54]
and Qian, Nantian , TITLE =
Margulis, Gregory A. and Qian, Nantian , TITLE =. Ergodic Theory Dynam. Systems , FJOURNAL =. 2001 , NUMBER =. doi:10.1017/S0143385701001109 , URL =
2001 doi
-
[55]
Hirsch, M. W. and Pugh, C. C. and Shub, M. , TITLE =. 1977 , PAGES =
1977
-
[56]
Seydoux, Guillaume , TITLE =. Trans. Amer. Math. Soc. , FJOURNAL =. 1994 , NUMBER =. doi:10.2307/2154997 , URL =
1994 doi
-
[57]
Zimmer's conjecture: Subexponential growth, measure rigidity, and strong property (T) , publisher =
Brown, Aaron and Fisher, David and Hurtado, Sebastian , keywords =. Zimmer's conjecture: Subexponential growth, measure rigidity, and strong property (T) , publisher =. 2016 , copyright =. doi:10.48550/ARXIV.1608.04995 , url =
- [58]
-
[59]
Brown, Aaron and Fisher, David and Hurtado, Sebastian , TITLE =. Invent. Math. , FJOURNAL =. 2020 , NUMBER =. doi:10.1007/s00222-020-00962-x , URL =
2020 doi
- [60]
-
[61]
Ergodic Theory Dynam
Connell, Chris and Nguyen, Thang and Spatzier, Ralf , TITLE =. Ergodic Theory Dynam. Systems , FJOURNAL =. 2022 , NUMBER =. doi:10.1017/etds.2021.116 , URL =
2022 doi
- [62]
-
[63]
2021 , eprint=
Stability for hyperbolic groups acting on boundary spheres , author=. 2021 , eprint=
2021
-
[64]
Fisher, David and Margulis, Gregory , TITLE =. Invent. Math. , FJOURNAL =. 2005 , NUMBER =. doi:10.1007/s00222-004-0437-5 , URL =
2005 doi
-
[65]
On discrete subgroups of
Weil, Andr\'. On discrete subgroups of. Ann. of Math. (2) , FJOURNAL =. 1962 , PAGES =. doi:10.2307/1970212 , URL =
1962 doi
-
[66]
Ergodic Theory Dynam
Qian, Nantian and Yue, Chengbo , TITLE =. Ergodic Theory Dynam. Systems , FJOURNAL =. 1998 , NUMBER =. doi:10.1017/S014338579810826X , URL =
1998 doi
-
[67]
Local rigidity of certain partially hyperbolic actions of product type , JOURNAL =
Ni. Local rigidity of certain partially hyperbolic actions of product type , JOURNAL =. 2001 , NUMBER =. doi:10.1017/S0143385701001560 , URL =
2001 doi
-
[68]
and Lewis, J
Katok, A. and Lewis, J. , TITLE =. Israel J. Math. , FJOURNAL =. 1991 , NUMBER =. doi:10.1007/BF02776025 , URL =
1991 doi
-
[69]
and Marco, J
de la Llave, R. and Marco, J. M. and Moriy\'. Canonical perturbation theory of. Ann. of Math. (2) , FJOURNAL =. 1986 , NUMBER =. doi:10.2307/1971334 , URL =
1986 doi
-
[70]
On local rigidity of partially hyperbolic affine
Damjanovi\'. On local rigidity of partially hyperbolic affine. J. Reine Angew. Math. , FJOURNAL =. 2019 , PAGES =. doi:10.1515/crelle-2016-0059 , URL =
2019 doi
-
[71]
Local rigidity of partially hyperbolic actions
Damjanovi\'. Local rigidity of partially hyperbolic actions. Int. Math. Res. Not. IMRN , FJOURNAL =. 2011 , NUMBER =. doi:10.1093/imrn/rnq252 , URL =
2011 doi
-
[72]
Damjanovic, Danijela and Katok, Anatole , TITLE =. J. Mod. Dyn. , FJOURNAL =. 2011 , NUMBER =. doi:10.3934/jmd.2011.5.203 , URL =
2011 doi
-
[73]
Local rigidity of partially hyperbolic actions
Damjanovi\'. Local rigidity of partially hyperbolic actions. Ann. of Math. (2) , FJOURNAL =. 2010 , NUMBER =. doi:10.4007/annals.2010.172.1805 , URL =
2010 doi
-
[74]
Local rigidity of restrictions of
Damjanovi\'. Local rigidity of restrictions of. C. R. Math. Acad. Sci. Paris , FJOURNAL =. 2007 , NUMBER =. doi:10.1016/j.crma.2007.03.009 , URL =
2007 doi
-
[75]
The local linearization problem for smooth
Cairns, Grant and Ghys, \'. The local linearization problem for smooth. Enseign. Math. (2) , FJOURNAL =. 1997 , NUMBER =
1997
-
[76]
Quasiconformal homeomorphisms and dynamics II: Structural stability implies hyperbolicity for
Sullivan, Dennis , journal =. Quasiconformal homeomorphisms and dynamics II: Structural stability implies hyperbolicity for. 1985 , number =
1985
-
[77]
, TITLE =
Zimmer, Robert J. , TITLE =. Proceedings of the. 1987 , MRCLASS =
1987
- [78]
-
[79]
Gorodnik, Alexander and Spatzier, Ralf , TITLE =. Geom. Topol. , FJOURNAL =. 2018 , NUMBER =. doi:10.2140/gt.2018.22.1227 , URL =
2018 doi
-
[80]
and Schroeder, V
Buyalo, S. and Schroeder, V. , TITLE =. Trans. Amer. Math. Soc. , FJOURNAL =. 2001 , NUMBER =. doi:10.1090/S0002-9947-00-02583-6 , URL =
2001 doi
-
[81]
Schroeder, Viktor , TITLE =. Math. Ann. , FJOURNAL =. 1986 , NUMBER =. doi:10.1007/BF01458013 , URL =
1986 doi
-
[82]
Croke, C. B. and Kleiner, B. , TITLE =. Geom. Funct. Anal. , FJOURNAL =. 2002 , NUMBER =. doi:10.1007/s00039-002-8255-7 , URL =
2002 doi
-
[83]
Eskin, Alex , TITLE =. J. Amer. Math. Soc. , FJOURNAL =. 1998 , NUMBER =. doi:10.1090/S0894-0347-98-00256-2 , URL =
1998 doi
-
[84]
Margulis, G. A. , TITLE =. Invent. Math. , FJOURNAL =. 1984 , NUMBER =. doi:10.1007/BF01388494 , URL =
1984 doi
-
[85]
and Raghunathan, M
Garland, H. and Raghunathan, M. S. , TITLE =. Ann. of Math. (2) , FJOURNAL =. 1970 , PAGES =. doi:10.2307/1970838 , URL =
1970 doi
-
[86]
Contributions to function theory (
Selberg, Atle , TITLE =. Contributions to function theory (. 1960 , MRCLASS =
1960
-
[87]
Calabi, Eugenio , TITLE =. Proc. 1961 , MRCLASS =
1961
-
[88]
On discrete subgroups of
Weil, Andr\'. On discrete subgroups of. Ann. of Math. (2) , FJOURNAL =. 1960 , PAGES =. doi:10.2307/1970140 , URL =
1960 doi
-
[89]
Cocycles, symplectic structures and intersection , Url =
Hamenst. Cocycles, symplectic structures and intersection , Url =. Geom. Funct. Anal. , Mrclass =. 1999 , Bdsk-File-1 =. doi:10.1007/s000390050082 , Fjournal =
1999 doi
-
[90]
2021 , eprint=
Medium-Scale Ricci Curvature for Hyperbolic Groups , author=. 2021 , eprint=
2021
-
[91]
Butler, Clark , TITLE =. J. Differential Geom. , FJOURNAL =. 2018 , NUMBER =. doi:10.4310/jdg/1525399216 , URL =
2018
-
[92]
Characterizing symmetric spaces by their
Butler, Clark , journal =. Characterizing symmetric spaces by their
-
[93]
Benveniste, E. J. , TITLE =. Geom. Funct. Anal. , FJOURNAL =. 2000 , NUMBER =. doi:10.1007/PL00001627 , URL =
2000 doi
-
[94]
Schmidt, Benjamin and Shankar, Krishnan and Spatzier, Ralf , TITLE =. Comment. Math. Helv. , FJOURNAL =. 2016 , NUMBER =. doi:10.4171/CMH/384 , URL =
2016 doi
-
[95]
Indiana Univ
Lin, Samuel , TITLE =. Indiana Univ. Math. J. , FJOURNAL =. 2018 , NUMBER =. doi:10.1512/iumj.2018.67.7427 , URL =
2018 doi
-
[96]
Margulis, G. A. and Mostow, G. D. , TITLE =. J. Anal. Math. , FJOURNAL =. 2000 , PAGES =. doi:10.1007/BF02791539 , URL =
2000 doi
-
[97]
Margulis, G. A. and Mostow, G. D. , TITLE =. Geom. Funct. Anal. , FJOURNAL =. 1995 , NUMBER =. doi:10.1007/BF01895673 , URL =
1995 doi
-
[98]
Fonction spectrale et valeurs propres d'une classe d'op
M. Fonction spectrale et valeurs propres d'une classe d'op. Comm. Partial Differential Equations , FJOURNAL =. 1976 , NUMBER =. doi:10.1080/03605307608820018 , URL =
1976 doi
-
[99]
Mitchell, John , TITLE =. J. Differential Geom. , FJOURNAL =. 1985 , NUMBER =
1985
-
[100]
Handbook of
Walsh, Cormac , TITLE =. Handbook of. 2014 , MRCLASS =
2014
-
[101]
Nguyen, Thang , TITLE =. Geom. Dedicata , FJOURNAL =. 2021 , PAGES =. doi:10.1007/s10711-020-00536-4 , URL =
2021 doi
-
[102]
Ergodic Theory Dynam
Connell, Chris and Nguyen, Thang and Spatzier, Ralf , TITLE =. Ergodic Theory Dynam. Systems , FJOURNAL =. 2020 , NUMBER =. doi:10.1017/etds.2018.113 , URL =
2020 doi
-
[103]
Sisto, Alessandro , TITLE =. Enseign. Math. (2) , FJOURNAL =. 2013 , NUMBER =. doi:10.4171/LEM/59-1-6 , URL =
2013 doi
-
[104]
and Spatzier, R
Katok, A. and Spatzier, R. J. , TITLE =. Tr. Mat. Inst. Steklova , FJOURNAL =. 1997 , NUMBER =
1997
-
[105]
2020 , eprint=
C^0 stability of boundary actions and inequivalent Anosov flows , author=. 2020 , eprint=
2020
-
[106]
Rigidit\'
Ghys, \'. Rigidit\'. Inst. Hautes \'. 1993 , PAGES =
1993
-
[107]
Yue, Cheng Bo , TITLE =. Math. Res. Lett. , FJOURNAL =. 1995 , NUMBER =. doi:10.4310/MRL.1995.v2.n3.a10 , URL =
1995 doi
-
[108]
2016 , PAGES =
Cornulier, Yves and de la Harpe, Pierre , TITLE =. 2016 , PAGES =. doi:10.4171/166 , URL =
2016 doi
-
[109]
Algebraic & Geometric Topology , NOTE =
Nguyen, Thang and Wang, Shi , TITLE =. Algebraic & Geometric Topology , NOTE =
-
[110]
Cheeger, Jeff and Naber, Aaron , TITLE =. Invent. Math. , FJOURNAL =. 2013 , NUMBER =. doi:10.1007/s00222-012-0394-3 , URL =
2013 doi
-
[111]
, TITLE =
Cheeger, Jeff and Colding, Tobias H. , TITLE =. J. Differential Geom. , FJOURNAL =. 1997 , NUMBER =
1997
-
[112]
Garland, Howard , TITLE =. Ann. of Math. (2) , FJOURNAL =. 1973 , PAGES =. doi:10.2307/1970829 , URL =
1973 doi
-
[113]
Acta Math
Sturm, Karl-Theodor , TITLE =. Acta Math. , FJOURNAL =. 2006 , NUMBER =. doi:10.1007/s11511-006-0003-7 , URL =
2006 doi
-
[114]
Acta Math
Sturm, Karl-Theodor , TITLE =. Acta Math. , FJOURNAL =. 2006 , NUMBER =. doi:10.1007/s11511-006-0002-8 , URL =
2006 doi
-
[115]
Ricci curvature for metric-measure spaces via optimal transport , JOURNAL =
Lott, John and Villani, C\'. Ricci curvature for metric-measure spaces via optimal transport , JOURNAL =. 2009 , NUMBER =. doi:10.4007/annals.2009.169.903 , URL =
2009 doi
- [116]
-
[117]
, TITLE =
Rotman, Joseph J. , TITLE =. 1995 , PAGES =. doi:10.1007/978-1-4612-4176-8 , URL =
1995 doi
-
[118]
Lohkamp, Joachim , TITLE =. Ann. of Math. (2) , FJOURNAL =. 1994 , NUMBER =. doi:10.2307/2118620 , URL =
1994 doi
-
[119]
Ollivier, Yann , TITLE =. C. R. Math. Acad. Sci. Paris , FJOURNAL =. 2007 , NUMBER =. doi:10.1016/j.crma.2007.10.041 , URL =
2007 doi
-
[120]
On the separation profile of infinite graphs , JOURNAL =
Benjamini, Itai and Schramm, Oded and Tim\'. On the separation profile of infinite graphs , JOURNAL =. 2012 , NUMBER =. doi:10.4171/GGD/168 , URL =
2012 doi
-
[121]
Ollivier, Yann , TITLE =. J. Funct. Anal. , FJOURNAL =. 2009 , NUMBER =. doi:10.1016/j.jfa.2008.11.001 , URL =
2009 doi
-
[122]
Probabilistic approach to geometry , SERIES =
Ollivier, Yann , TITLE =. Probabilistic approach to geometry , SERIES =. 2010 , MRCLASS =. doi:10.2969/aspm/05710343 , URL =
2010
-
[123]
Analysis and geometry of metric measure spaces , SERIES =
Ollivier, Yann , TITLE =. Analysis and geometry of metric measure spaces , SERIES =. 2013 , MRCLASS =
2013
-
[124]
Cheeger, Jeff and Gromoll, Detlef , TITLE =. J. Differential Geometry , FJOURNAL =. 1971/72 , PAGES =
1971
-
[125]
Differential Geom
Wilking, Burkhard , TITLE =. Differential Geom. Appl. , FJOURNAL =. 2000 , NUMBER =. doi:10.1016/S0926-2245(00)00030-9 , URL =
2000 doi
-
[126]
Gromov, Mikhael , TITLE =. Inst. Hautes \'. 1981 , PAGES =
1981
-
[127]
Conjugation curvature for Cayley graphs , author=. J. Topol. Anal. , year=. 1712.02484 , archivePrefix=
-
[128]
Modern dynamical systems and applications , PAGES =
Abels, Herbert and Margulis, Gregory , TITLE =. Modern dynamical systems and applications , PAGES =. 2004 , MRCLASS =
2004
-
[129]
and Courtois, G
Besson, G. and Courtois, G. and Gallot, S. , TITLE =. Invent. Math. , FJOURNAL =. 1991 , NUMBER =. doi:10.1007/BF01239520 , URL =
1991 doi
-
[130]
Ballmann, Werner , TITLE =. Ann. of Math. (2) , FJOURNAL =. 1985 , NUMBER =. doi:10.2307/1971331 , URL =
1985 doi
-
[131]
1995 , PAGES =
Ballmann, Werner , TITLE =. 1995 , PAGES =. doi:10.1007/978-3-0348-9240-7 , URL =
1995 doi
-
[132]
arxiv , YEAR =
Brown, Aaron , TITLE =. arxiv , YEAR =
-
[133]
and Sisto, Alessandro , TITLE =
Behrstock, Jason and Hagen, Mark F. and Sisto, Alessandro , TITLE =. Geom. Topol. , FJOURNAL =. 2017 , NUMBER =. doi:10.2140/gt.2017.21.1731 , URL =
2017 doi
-
[134]
Bonk, Mario and Kleiner, Bruce , TITLE =. J. Differential Geom. , FJOURNAL =. 2002 , NUMBER =
2002
-
[136]
Flots d'
Benoist, Yves and Foulon, Patrick and Labourie, Fran. Flots d'. J. Amer. Math. Soc. , FJOURNAL =. 1992 , NUMBER =. doi:10.2307/2152750 , URL =
1992 doi
-
[137]
Bourdon, Marc , TITLE =. Inst. Hautes \'. 1996 , PAGES =
1996
-
[138]
Boyer, Adrien , TITLE =
-
[139]
Groups Geom
Breuillard, Emmanuel , TITLE =. Groups Geom. Dyn. , FJOURNAL =. 2014 , NUMBER =. doi:10.4171/GGD/244 , URL =
2014 doi
-
[140]
Burns, Keith and Spatzier, Ralf , TITLE =. Inst. Hautes \'. 1987 , PAGES =
1987
-
[141]
, TITLE =
Burago, D. , TITLE =. Seminar on. 1994 , MRCLASS =. doi:10.1007/978-3-0348-7515-8_7 , URL =
1994 doi
-
[142]
and Katok, A
Burns, K. and Katok, A. , TITLE =. Ergodic Theory Dynam. Systems , FJOURNAL =. 1985 , NUMBER =. doi:10.1017/S0143385700002935 , URL =
1985 doi
-
[143]
and Ruane, K
Chatterji, I. and Ruane, K. , TITLE =. Geom. Funct. Anal. , FJOURNAL =. 2005 , NUMBER =. doi:10.1007/s00039-005-0508-9 , URL =
2005 doi
-
[144]
Connell, Christopher , TITLE =. Geom. Dedicata , FJOURNAL =. 2002 , PAGES =. doi:10.1023/A:1020307604978 , URL =
2002 doi
-
[145]
1994 , PAGES =
Connes, Alain , TITLE =. 1994 , PAGES =
1994
-
[146]
Constantine, David , TITLE =. J. Mod. Dyn. , FJOURNAL =. 2008 , NUMBER =. doi:10.3934/jmd.2008.2.719 , URL =
2008 doi
-
[147]
de la Harpe, Pierre , TITLE =. C. R. Acad. Sci. Paris S\'. 1988 , NUMBER =
1988
-
[148]
Displacing representations and orbit maps , BOOKTITLE =
Delzant, Thomas and Guichard, Olivier and Labourie, Fran. Displacing representations and orbit maps , BOOKTITLE =. 2011 , MRCLASS =
2011
-
[149]
Quasi-isometric classification of non-uniform lattices in semisimple groups of higher rank , JOURNAL =
Dru. Quasi-isometric classification of non-uniform lattices in semisimple groups of higher rank , JOURNAL =. 2000 , NUMBER =. doi:10.1007/s000390050011 , URL =
2000 doi
-
[150]
Relatively hyperbolic groups with rapid decay property , JOURNAL =
Dru. Relatively hyperbolic groups with rapid decay property , JOURNAL =. 2005 , NUMBER =. doi:10.1155/IMRN.2005.1181 , URL =
2005
-
[151]
Tree-graded spaces and asymptotic cones of groups , NOTE =
Dru. Tree-graded spaces and asymptotic cones of groups , NOTE =. Topology , FJOURNAL =. 2005 , NUMBER =. doi:10.1016/j.top.2005.03.003 , URL =
2005 doi
-
[152]
Groups acting on tree-graded spaces and splittings of relatively hyperbolic groups , JOURNAL =
Dru. Groups acting on tree-graded spaces and splittings of relatively hyperbolic groups , JOURNAL =. 2008 , NUMBER =. doi:10.1016/j.aim.2007.08.012 , URL =
2008 doi
-
[153]
Eskin, Alex and Farb, Benson , TITLE =. J. Amer. Math. Soc. , FJOURNAL =. 1997 , NUMBER =. doi:10.1090/S0894-0347-97-00238-5 , URL =
1997 doi
-
[154]
Farb, Benson and Schwartz, Richard , TITLE =. J. Differential Geom. , FJOURNAL =. 1996 , NUMBER =
1996
-
[155]
Fisher, David and Nguyen, Thang , TITLE =. Comment. Math. Helv. , FJOURNAL =. 2020 , NUMBER =. doi:10.4171/cmh/480 , URL =
2020 doi
-
[156]
Fisher, David and Nguyen, Thang and van Limbeek, Wouter , TITLE =. Adv. Math. , FJOURNAL =. 2019 , PAGES =. doi:10.1016/j.aim.2019.02.015 , URL =
2019 doi
-
[157]
Fisher, David and Whyte, Kevin , TITLE =. Geom. Topol. , FJOURNAL =. 2018 , NUMBER =. doi:10.2140/gt.2018.22.3049 , URL =
2018 doi
-
[158]
Foulon, Patrick , title =. C. R. Acad. Sci. Paris S. 1994 , volume =
1994
-
[159]
Fujiwara, Koji , TITLE =. J. Topol. Anal. , FJOURNAL =. 2015 , NUMBER =. doi:10.1142/S1793525315500132 , URL =
2015 doi
-
[160]
Proceedings of the
Gromov, Mikhael , TITLE =. Proceedings of the. 1984 , MRCLASS =
1984
-
[161]
, TITLE =
Gromov, M. , TITLE =. Essays in group theory , SERIES =. 1987 , MRCLASS =. doi:10.1007/978-1-4613-9586-7_3 , URL =
1987 doi
-
[162]
Gromov, Michael , TITLE =. G\'. 1988 , MRCLASS =
1988
-
[163]
, TITLE =
Gromov, M. , TITLE =. Geometric group theory,. 1993 , MRCLASS =
1993
-
[164]
Israel J
Groves, Daniel and Manning, Jason Fox , TITLE =. Israel J. Math. , FJOURNAL =. 2008 , PAGES =. doi:10.1007/s11856-008-1070-6 , URL =
2008 doi
-
[165]
Haagerup, Uffe , TITLE =. Invent. Math. , FJOURNAL =. 1978/79 , NUMBER =. doi:10.1007/BF01410082 , URL =
1978 doi
-
[166]
A geometric characterization of negatively curved locally symmetric spaces , JOURNAL =
Hamenst\". A geometric characterization of negatively curved locally symmetric spaces , JOURNAL =. 1991 , NUMBER =
1991
-
[167]
Ergodic Theory Dynam
Hasselblatt, Boris , TITLE =. Ergodic Theory Dynam. Systems , FJOURNAL =. 1994 , NUMBER =. doi:10.1017/S0143385700008105 , URL =
1994 doi
-
[168]
and Pugh, Charles C
Hirsch, Morris W. and Pugh, Charles C. , TITLE =. Bull. Amer. Math. Soc. , FJOURNAL =. 1969 , PAGES =. doi:10.1090/S0002-9904-1969-12184-1 , URL =
1969 doi
-
[169]
Hirsch, M. W. and Pugh, C. C. and Shub, M. , title =. Bull. Amer. Math. Soc. , year =
-
[170]
Jolissaint, Paul , TITLE =. C. R. Acad. Sci. Paris S\'. 1986 , NUMBER =
1986
-
[171]
Kanai, Masahiko , TITLE =. Tokyo J. Math. , FJOURNAL =. 1983 , NUMBER =. doi:10.3836/tjm/1270214332 , URL =
1983
-
[172]
Topology , FJOURNAL =
Kim, Inkang , TITLE =. Topology , FJOURNAL =. 2001 , NUMBER =. doi:10.1016/S0040-9383(00)00012-4 , URL =
2001 doi
-
[173]
Kleiner, Bruce and Leeb, Bernhard , TITLE =. Invent. Math. , FJOURNAL =. 2006 , NUMBER =. doi:10.1007/s00222-005-0471-y , URL =
2006 doi
-
[174]
Kleiner, Bruce and Leeb, Bernhard , TITLE =. Inst. Hautes \'. 1997 , PAGES =
1997
-
[175]
Lafforgue, Vincent , TITLE =. J. Lie Theory , FJOURNAL =. 2000 , NUMBER =
2000
-
[176]
Quanta of maths , SERIES =
Lafforgue, Vincent , TITLE =. Quanta of maths , SERIES =. 2010 , MRCLASS =
2010
-
[177]
Lubotzky, Alexander and Mozes, Shahar and Raghunathan, M. S. , TITLE =. Inst. Hautes \'. 2000 , PAGES =
2000
-
[178]
arxiv , YEAR =
Leuzinger, Enrico and Young, Robert , TITLE =. arxiv , YEAR =
-
[179]
Maher, Joseph and Tiozzo, Giulio , TITLE =. J. Reine Angew. Math. , FJOURNAL =. 2018 , PAGES =. doi:10.1515/crelle-2015-0076 , URL =
2018 doi
-
[180]
Margulis, G. A. , TITLE =. 1991 , PAGES =. doi:10.1007/978-3-642-51445-6 , URL =
1991 doi
-
[181]
Mostow, G. D. , TITLE =. Inst. Hautes \'. 1968 , PAGES =
1968
-
[182]
, TITLE=
Melnick, K. , TITLE=. Ergodic Theory Dynam. Systems , YEAR =
-
[183]
and Sawicki, Damian , TITLE =
Nowak, Piotr W. and Sawicki, Damian , TITLE =. Proc. Amer. Math. Soc. , FJOURNAL =. 2017 , NUMBER =. doi:10.1090/proc/13258 , URL =
2017 doi
-
[184]
, TITLE =
Osin, Denis V. , TITLE =. Invent. Math. , FJOURNAL =. 2007 , NUMBER =. doi:10.1007/s00222-006-0012-3 , URL =
2007 doi
-
[185]
Otal, Jean-Pierre , TITLE =. Ann. of Math. (2) , FJOURNAL =. 1990 , NUMBER =. doi:10.2307/1971511 , URL =
1990 doi
-
[186]
Pansu, Pierre , TITLE =. Ann. of Math. (2) , FJOURNAL =. 1989 , NUMBER =. doi:10.2307/1971484 , URL =
1989 doi
-
[187]
Prasad, Gopal , TITLE =. Invent. Math. , FJOURNAL =. 1973 , PAGES =. doi:10.1007/BF01418789 , URL =
1973 doi
-
[188]
and Robertson, G
Ramagge, J. and Robertson, G. and Steger, T. , TITLE =. Geom. Funct. Anal. , FJOURNAL =. 1998 , NUMBER =. doi:10.1007/s000390050071 , URL =
1998 doi
-
[189]
, TITLE =
Croke, Christopher B. , TITLE =. Comment. Math. Helv. , FJOURNAL =. 1990 , NUMBER =. doi:10.1007/BF02566599 , URL =
1990 doi
-
[190]
Schwartz, Richard Evan , TITLE =. Inst. Hautes \'. 1995 , PAGES =
1995
-
[191]
Acta Math
Schwartz, Richard Evan , TITLE =. Acta Math. , FJOURNAL =. 1996 , NUMBER =. doi:10.1007/BF02392599 , URL =
1996 doi
-
[192]
1974 , PAGES =
Tits, Jacques , TITLE =. 1974 , PAGES =
1974
-
[193]
Young, Robert , TITLE =. Ann. of Math. (2) , FJOURNAL =. 2013 , NUMBER =. doi:10.4007/annals.2013.177.3.4 , URL =
2013 doi
-
[194]
van Limbeek , Journal =
W. van Limbeek , Journal =
-
[195]
van Limbeek , Note =
W. van Limbeek , Note =. Classification of normally and finitely non-co-
-
[196]
Shulkin and W
J. Shulkin and W. van Limbeek , Journal =. The fundamental theorem of affine geometry on tori , Volume =
-
[197]
van Limbeek and A
W. van Limbeek and A. Zimmer , Note =. Rigidity of convex divisible domain in flag manifolds , Year =
-
[198]
van Limbeek , Journal =
W. van Limbeek , Journal =. Isometry types of frame bundles , Volume =
-
[199]
van Limbeek , Journal =
W. van Limbeek , Journal =. Symmetry gaps in Riemannian geometry and minimal orbifolds , Volume =
-
[200]
van Limbeek , Journal =
W. van Limbeek , Journal =. Riemannian manifolds with local symmetry , Volume =
-
[201]
Lafont and B
J.-F. Lafont and B. Schmidt and W. van Limbeek , Journal =. Quasicircle boundaries and exotic almost-isometries , Volume =
-
[202]
Raghunathan , Publisher =
M. Raghunathan , Publisher =. Discrete Subgroups of Lie Groups , Year =
-
[203]
Witte Morris , Note =
D. Witte Morris , Note =
-
[204]
Onishchik and E
A. Onishchik and E. Vinberg , Publisher =. Lie Groups and Lie Algebras, vol. 2: Discrete Subgroups of Lie Groups and Cohomologies of Lie Groups and Lie Algebras , Year =
-
[205]
Kobayashi , Publisher =
S. Kobayashi , Publisher =. Transformation Groups in Differential Geometry , Year =
-
[206]
Gromov , Publisher =
M. Gromov , Publisher =. Metric structures for Riemannian and non-Riemannian spaces , Year =
-
[207]
Burago and Y
D. Burago and Y. Burago and S. Ivanov , Publisher =. A course in metric geometry , Volume =
-
[208]
Bredon , Publisher =
G. Bredon , Publisher =. Introduction to Compact Transformation Groups , Year =
-
[209]
Spanier , Publisher =
E. Spanier , Publisher =. Algebraic Topology , Year =
-
[210]
Knapp , Publisher =
A. Knapp , Publisher =. Lie Groups Beyond an Introduction , Year =
-
[211]
Mostow , Number =
G. Mostow , Number =. Strong rigidity of locally symmetric spaces , Year =
-
[212]
Bochner and K
S. Bochner and K. Yano , Number =. Curvature and
-
[213]
Petersen , Number =
P. Petersen , Number =. Riemannian geometry , Year =
-
[214]
Farb and S
B. Farb and S. Weinberger , Journal =
-
[215]
Farb and S
B. Farb and S. Weinberger , Booktitle =. Hidden symmetries and arithmetic manifolds , Volume =
-
[216]
Eberlein , Journal =
P. Eberlein , Journal =. Lattices in spaces of nonpositive curvature , Volume =
-
[217]
Eberlein , Journal =
P. Eberlein , Journal =. Isometry groups of simply connected manifolds of nonpositive curvature II , Volume =
-
[218]
Frankel , Journal =
S. Frankel , Journal =. Locally symmetric and rigid factors for complex manifolds via harmonic maps , Volume =
-
[219]
Avramidi , Journal =
G. Avramidi , Journal =. Periodic Flats and group actions on locally symmetric spaces , Volume =
-
[220]
Frankel , Journal =
S. Frankel , Journal =. Complex geometry of convex domains that cover varieties , Volume =
-
[221]
Nadel , Journal =
A. Nadel , Journal =. Semisimplicity of the group of biholomorphisms of the universal covering of a compact complex manifold with ample canonical bundle , Volume =
-
[222]
Melnick , Journal =
K. Melnick , Journal =. Isometric actions of Heisenberg groups on compact Lorentz manifolds , Volume =
-
[223]
Zeghib , Journal =
A. Zeghib , Journal =. Isometry groups and geodesic foliations of
-
[224]
Melnick , Journal =
K. Melnick , Journal =. Compact Lorentz manifolds with local symmetry , Volume =
-
[225]
Deffaf, K
M. Deffaf, K. Melnick, and A. Zeghib , Journal =. Actions of noncompact semisimple groups on Lorentz manifolds , Volume =
-
[226]
Borel , Booktitle =
A. Borel , Booktitle =. On periodic maps of certain
-
[227]
Borel , Journal =
A. Borel , Journal =. Compact
-
[228]
Schoen and S
R. Schoen and S. Yau , Journal =. Compact group actions and the topology of manifolds with nonpositive curvature , Volume =
-
[229]
Starkov , Journal =
A. Starkov , Journal =. A counterexample to a theorem on lattices in Lie groups , Year =
-
[230]
Wu , Journal =
T. Wu , Journal =. A note on a theorem on lattices in Lie groups , Volume =
-
[231]
Mostow , Journal =
G. Mostow , Journal =. Equivariant embeddings in Euclidean space , Volume =
-
[232]
Palais , Journal =
R. Palais , Journal =. Imbedding of compact differentiable transformation groups in orthogonal representations , Volume =
-
[233]
Palais , Journal =
R. Palais , Journal =. On the existence of slices for actions of non-compact Lie groups , Volume =
-
[234]
Myers and N
S. Myers and N. Steenrod , Journal =. The Group of Isometries of a Riemannian Manifold , Vol =
-
[235]
Hurwitz , Journal =
A. Hurwitz , Journal =
-
[236]
Huber , Journal =
H. Huber , Journal =
-
[237]
Katsuda , Journal =
A. Katsuda , Journal =. The isometry groups of compact manifolds with negative
-
[238]
Maeda , Journal =
M. Maeda , Journal =. The isometry groups of compact manifolds with non-positive curvature , Volume =
-
[239]
Im Hof , Journal =
H.C. Im Hof , Journal =
-
[240]
Dai and Z
X. Dai and Z. Shen and G. Wei , Journal =. Negative
-
[241]
Lohkamp , Journal =
J. Lohkamp , Journal =. Metrics of Negative Ricci Curvature , Volume =
-
[242]
Fukaya , Booktitle =
K. Fukaya , Booktitle =. Hausdorff convergence of Riemannian manifolds and its applications , Year =
-
[243]
Fukaya , Journal =
K. Fukaya , Journal =. Theory of convergence for Riemannian orbifolds , Volume =
-
[244]
Fukaya and T
K. Fukaya and T. Yamaguchi , Journal =. Fundamental groups of almost negatively curved manifolds , Volume =
-
[245]
Cappell and S
S. Cappell and S. Weinberger and M. Yan , Journal =. Closed aspherical manifolds with center , Vol =
-
[246]
T. T. Nguyen Phan , Journal =
-
[247]
Kazhdan and G
D. Kazhdan and G. Margulis , Journal =. A proof of
-
[248]
Gromov , Journal =
M. Gromov , Journal =. Almost flat manifolds , Volume =
-
[249]
Gromov , Journal =
M. Gromov , Journal =. Manifolds of negative curvature , Volume =
-
[250]
Calabi and P
S. Calabi and P. Hartman , Journal =. On the smoothness of isometries , Volume =
-
[251]
Lytchak and A
A. Lytchak and A. Yaman , Journal =. On
-
[252]
Taylor , Journal =
M. Taylor , Journal =. Existence and regularity of isometries , Volume =
-
[253]
Bochner and D
S. Bochner and D. Montgomery , Journal =. Locally compact groups of differentiable transformations , Volume =
-
[254]
Yamabe , Journal =
H. Yamabe , Journal =. A generalization of a theorem of
-
[255]
Montgomery , Journal =
D. Montgomery , Journal =. Topological groups of differentiable transformations , Volume =
-
[256]
Bishop , Journal =
R. Bishop , Journal =. A relation between volume, mean curvature and diameter , Volume =
-
[257]
Hartman , Journal =
P. Hartman , Journal =. On the local uniqueness of geodesics , Volume =
-
[258]
Hartman and A
P. Hartman and A. Wintner , Journal =. On the problem of geodesics in the small , Volume =
-
[259]
Berger , Journal =
M. Berger , Journal =. Une borne inf
-
[260]
Zeghib , Journal =
A. Zeghib , Journal =
-
[261]
Cheeger , Journal =
J. Cheeger , Journal =. Finiteness theorems for
-
[262]
Cheeger and M
J. Cheeger and M. Gromov , Journal =. Collapsing
-
[263]
Cheeger and K
J. Cheeger and K. Fukaya and M. Gromov , Journal =. Nilpotent structures and invariant metrics on collapsed manifolds , Volume =
-
[264]
Cheeger and X
J. Cheeger and X. Rong , Journal =. Collapsed
-
[265]
Cheeger and X
J. Cheeger and X. Rong , Journal =. Existence of polarized
-
[266]
Anderson , Journal =
M. Anderson , Journal =. Convergence and rigidity of manifolds under
-
[267]
Vilms , Journal =
J. Vilms , Journal =. Totally Geodesic Maps , Volume =
-
[268]
Wall , Journal =
C. Wall , Journal =. Finiteness obstructions for
-
[269]
Siegel , Journal =
C. Siegel , Journal =. Some Remarks on Discontinuous Groups , Volume =
-
[270]
Kerckhoff , Journal =
S. Kerckhoff , Journal =. The Nielsen Realization Problem , Volume =
-
[271]
Takagi and M
H. Takagi and M. Yawata , Journal =. Infinitesimal isometries of frame bundles with a natural
-
[272]
K. J. Falconer and D. T. Marsh , Journal =. Classification of quasi-circles by
-
[273]
K. J. Falconer and D. T. Marsh , Journal =. On the Lipschitz equivalence of Cantor sets , Volume =
-
[274]
Gabai , Journal =
D. Gabai , Journal =. Convergence groups are
-
[275]
Bonk and O
M. Bonk and O. Schramm , Journal =. Embeddings of
-
[276]
Cooper and T
D. Cooper and T. Pignataro , Journal =. On the shape of Cantor sets , Volume =
-
[277]
Kar and J.-F
A. Kar and J.-F. Lafont and B. Schmidt , Journal =
-
[278]
Farrell and L
T. Farrell and L. Jones , Journal =. Examples of expanding endomorphisms on exotic tori , Volume =
-
[279]
Shub , Journal =
M. Shub , Journal =. Expanding maps , Volume =
-
[280]
, Coden =
Fujimoto, Y. , Coden =. Endomorphisms of smooth projective 3-folds with non-negative. Publ. Res. Inst. Math. Sci. , Number =. 2002 , Bdsk-Url-1 =
2002
-
[281]
and Zhang, D.-Q
Nakayama, N. and Zhang, D.-Q. , Journal =. Building blocks of
-
[282]
, Journal =
Beauville, A. , Journal =. Endomorphisms of hypersurfaces and other manifolds , Year =
-
[283]
Non-algebraic compact
H. Non-algebraic compact. Sci. China Math. , Number =
-
[284]
, Date-Added =
Montgomery, D. , Date-Added =. Topological groups of differentiable transformations , Volume =. Ann. of Math. (2) , Mrclass =. 1945 , Bdsk-Url-1 =
1945
-
[285]
, Date-Added =
Blanchard, A. , Date-Added =. Sur les vari. Ann. Sci. Ecole Norm. Sup. (3) , Mrclass =. 1956 , Bdsk-Url-1 =
1956
-
[286]
, Coden =
Biswas, I. , Coden =. On abelian principal bundles , Url =. Arch. Math. (Basel) , Mrclass =. 2007 , Bdsk-Url-1 =. doi:10.1007/s00013-006-1712-z , Fjournal =
2007 doi
-
[287]
, Booktitle =
Shicheng W. , Booktitle =. Non-zero degree maps between 3-manifolds , Year =
-
[288]
and Wang, S
Yu, F. and Wang, S. , Coden =. Covering degrees are determined by graph manifolds involved , Url =. Comment. Math. Helv. , Mrclass =. 1999 , Bdsk-Url-1 =. doi:10.1007/s000140050087 , Fjournal =
1999 doi
-
[289]
Farrell, F. T. and Hsiang, W. C. , Date-Added =. The topological-. Invent. Math. , Mrclass =. 1978 , Bdsk-Url-1 =
1978
-
[290]
Whitehead, J. H. C. , Date-Added =. Combinatorial homotopy. Bull. Amer. Math. Soc. , Mrclass =. 1949 , Bdsk-Url-1 =
1949
-
[291]
, Coden =
Carlsson, G. , Coden =. On the homology of finite free. Invent. Math. , Mrclass =. 1983 , Bdsk-Url-1 =. doi:10.1007/BF01388534 , Fjournal =
1983 doi
-
[292]
, Date-Added =
Robinson, D. , Date-Added =. A course in the theory of groups , Url =. 1996 , Bdsk-Url-1 =. doi:10.1007/978-1-4419-8594-1 , Edition =
1996 doi
-
[293]
On closed abelian subgroups of real
W. On closed abelian subgroups of real. J. Lie Theory , Mrclass =. 1997 , Bdsk-Url-1 =
1997
-
[294]
, Date-Added =
Fujiki, A. , Date-Added =. On automorphism groups of compact. Invent. Math. , Mrclass =. 1978 , Bdsk-Url-1 =
1978
-
[295]
Chernikov , Date-Added =
S.N. Chernikov , Date-Added =. On locally solvable groups satisfying a minimality condition for subgroups , Volume =. Matem. Sb. , Number =
-
[296]
Ol'shanskii, A. Yu. , Date-Added =. An infinite group with subgroups of prime orders , Volume =. Izv. Akad. Nauk SSSR Ser. Mat. , Mrclass =. 1980 , Bdsk-Url-1 =
1980
-
[297]
and Pete, G
Nekrashevych, V. and Pete, G. , Date-Added =. Scale-invariant groups , Url =. Groups Geom. Dyn. , Mrclass =. 2011 , Bdsk-Url-1 =. doi:10.4171/GGD/119 , Fjournal =
2011 doi
-
[298]
and Kalinin, B
Fisher, D. and Kalinin, B. and Spatzier, R. , Date-Added =. Global rigidity of higher rank. J. Amer. Math. Soc. , Mrclass =. 2013 , Bdsk-Url-1 =. doi:10.1090/S0894-0347-2012-00751-6 , Fjournal =
2013 doi
-
[299]
Gradings on
Cornulier, Yves , Fjournal =. Gradings on. Bull. Soc. Math. France , Mrclass =
-
[300]
Farrell, F. T. and Jones, L. E. , Date-Added =. Examples of expanding endomorphisms on exotic tori , Volume =. Invent. Math. , Mrclass =. 1978 , Bdsk-Url-1 =
1978
Reviewed August 2, 2026 · model on record in the stance chip above.
Discussion (0). Continue with ORCID to comment.