Analysis on fibred cusp spaces

arxiv: 2507.15467 · v2 · submitted 2025-07-21 · 🧮 math.DG · math.AP· math.SP

Analysis on fibred cusp spaces

Daniel Grieser , \'Alvaro S\'anchez-Hern\'andez , Boris Vertman This is my paper

Pith reviewed 2026-05-19 04:19 UTC · model grok-4.3

classification 🧮 math.DG math.APmath.SP

keywords fibred cusp spacesspectral geometryanalytic torsionindex theoryboundary value problemsmicrolocal analysisresolventheat kernel

0 comments p. Extension

The pith

Fibred cusp spaces receive a unified microlocal treatment for spectral geometry and boundary problems in both incomplete and complete settings.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper surveys analytic and geometric results on fibred cusp spaces, a broad class of non-compact Riemannian manifolds that includes the regular parts of spaces with incomplete cusp singularities as well as complete manifolds with asymptotically hyperbolic cusp or Euclidean structures at infinity. It covers topics in spectral geometry such as analytic torsion and index theory together with boundary value problems. The exposition stresses shared features and distinctions between the incomplete and various complete cases. The foundation is a careful microlocal analysis of the resolvent and heat kernel that is presented as applying across these settings. A sympathetic reader cares because the survey assembles a coherent picture for analysis on manifolds that appear in many geometric and physical contexts.

Core claim

The authors show that fibred cusp spaces admit a uniform analytic framework in which microlocal analysis of the resolvent and heat kernel yields results on analytic torsion, index theory, and boundary value problems, while making explicit both the common structures and the differences between incomplete cusp singularities and the various complete asymptotic models at infinity.

What carries the argument

Microlocal analysis of the resolvent and heat kernel on fibred cusp spaces, which supplies the estimates and expansions needed to treat spectral and index questions uniformly across incomplete and complete configurations.

Load-bearing premise

The microlocal analysis of the resolvent and heat kernel provides a uniform foundation that applies equally well across incomplete cusp singularities and the different complete asymptotic structures without requiring case-by-case adjustments that break the unified framework.

What would settle it

A concrete example in which the resolvent or heat kernel on an incomplete cusp space requires fundamentally different microlocal constructions than those used for a complete asymptotically hyperbolic cusp space would show that the uniform foundation does not hold.

Figures

Figures reproduced from arXiv: 2507.15467 by \'Alvaro S\'anchez-Hern\'andez, Boris Vertman, Daniel Grieser.

**Figure 1.** Figure 1: Three instances of fibred cusps. On the left, we have an incomplete cusp with fibre S 1 . In the middle, we start with a fundamental domain SL(2, R)/SL(2, Z) in the upper half plane model of hyperbolic space with the hyperbolic metric dz2+dw2 w2 and compactify at large w by introducing the coordinate x = 1 w , obtaining a model hyperbolic cusp. On the right, we compactify the large end of a cone dr2 + r 2d… view at source ↗

**Figure 2.** Figure 2: ϕ-double space depicted for X = R+ (so ∂X = {0} has trivial base and fibre). First the corner {(0, 0)} = (∂X) 2 ⊂ X2 is blown up, which separates lines arriving at the origin from different directions (note how the green is separated from the orange and blue ones by the new face with coordinate t = x ′ x , since curves x ′ = t1x + O(x 2 ) and x ′ = t2x + O(x 2 ) land at the point of the front face with t =… view at source ↗

**Figure 3.** Figure 3: Resolvent blow-up space X2 κ,ϕ The blow-up is obtained as follows. First, one blows up the codimension 3 corner ∂X × ∂X × {0}, which defines a new boundary hypersurface bf0. Then one blows up the codimension 2 corners X × ∂X × {0}, ∂X × X × {0} and ∂X × ∂X × R+, which define new boundary faces lb0, rb0 and bf, respectively. Next we blow up the (lifted) interior fibre diagonal diagϕ,int × R+ = {(p, q, κ) ∈ … view at source ↗

**Figure 4.** Figure 4: Heat blow-up space for 0-ϕ-metrics (compare [TV22, [PITH_FULL_IMAGE:figures/full_fig_p020_4.png] view at source ↗

**Figure 5.** Figure 5: Heat blow-up space for 1-ϕ-metrics (compare [Vai01, [PITH_FULL_IMAGE:figures/full_fig_p021_5.png] view at source ↗

**Figure 6.** Figure 6: Expected heat blow-up space for 2-ϕ-metrics 6.3. When is ∂/ self-adjoint and Fredholm? A word on self-adjointness and Fredholmness of the respective Dirac operators: • For incomplete spaces (as it is the case for c = 2), (essential) self-adjointness is not a given and there could be many self-adjoint extensions. The minimal and 21 [PITH_FULL_IMAGE:figures/full_fig_p021_6.png] view at source ↗

**Figure 7.** Figure 7: Compactified heat blow-up space for 0-ϕ-metrics (compare [PITH_FULL_IMAGE:figures/full_fig_p022_7.png] view at source ↗

**Figure 8.** Figure 8: An example of a ϕ-bc-manifold X (exterior of the central picture) and how it arises via blow-up from a singular space (exterior of left picture). Local coordinates are polar coordinates in the tangency plane (x = radius, y = angle), and z ∈ [−1, 1] when parametrizing the left/right direction by p(x)z where p(x) ∼ const x 2 as x → 0, with z = ±1 corresponding to points on the spheres. Correspondingly, the r… view at source ↗

read the original abstract

We give a survey of analytic and geometric results on `fibred cusp spaces', a large class of non-compact Riemannian manifolds which include the regular parts of singular spaces with incomplete cusp singularities as well as complete spaces with asymptotically hyperbolic cusp or asymptotically Euclidean structures at infinity. These results cover topics in spectral geometry, in particular analytic torsion and index theory, and boundary value problems. The underlying tools include a careful microlocal analysis of the resolvent and the heat kernel. We include an exposition of the geometric and analytic foundations and sketch the ideas of the proofs of the main theorems. Special emphasis is put on the common features of and the differences between the incomplete and various kinds of complete settings.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Desk Editor's Note private letter to a colleague

This is a competent survey that organizes existing results on fibred cusp spaces but adds no new theorems.

read the letter

Hi, the main takeaway is that this paper is a survey compiling analytic and geometric results on fibred cusp spaces rather than proving anything new. It covers spectral geometry topics such as analytic torsion and index theory, along with boundary value problems, for both incomplete cusp singularities and complete asymptotically hyperbolic or Euclidean structures. The authors rely on microlocal analysis of the resolvent and heat kernel, sketch proof ideas from prior work, and highlight common features alongside the differences between the incomplete and complete cases. What the paper does well is to lay out the geometric foundations in one place and show how a shared analytic toolkit applies across these settings while explicitly noting where adaptations are required. That comparative angle can help readers connect scattered results in the literature without having to reconstruct the connections themselves. The sketches of proofs and the emphasis on foundations seem like a practical way to make the material more accessible to people already working in this area. The soft spots are limited and mostly inherent to the survey format. The value depends on how accurately and completely the summaries represent the cited theorems, and the abstract gives no detailed evidence on that point. The weakest assumption mentioned in the reader's note about a uniform foundation across settings looks manageable because the paper itself discusses differences and adaptations rather than claiming perfect uniformity. No load-bearing new derivation is at risk here. This paper is mainly for specialists in geometric analysis or microlocal methods on non-compact and singular manifolds who want an organized overview or a quick way to compare approaches. A reader already familiar with some of the background will get the most from the comparisons. It is not aimed at outsiders or at anyone seeking original theorems or broad new applications. I would bring it to a reading group if the group includes people working on spectral invariants or analysis on singular spaces, as it could prompt useful discussion of the current state of the literature. I would not cite it in my own work in the next year because it contains no new results. It does deserve serious peer review because a careful survey of this type can clarify the field and serve as a reference point.

Referee Report

0 major / 2 minor

Summary. The manuscript surveys analytic and geometric results on fibred cusp spaces, a class of non-compact Riemannian manifolds that includes both the regular parts of singular spaces with incomplete cusp singularities and complete spaces with asymptotically hyperbolic cusp or asymptotically Euclidean structures at infinity. It addresses topics in spectral geometry (analytic torsion, index theory) and boundary value problems, relying on microlocal analysis of the resolvent and heat kernel. The text sketches geometric and analytic foundations, outlines proof ideas for main theorems, and stresses both shared features and distinctions between the incomplete and various complete asymptotic regimes.

Significance. A well-executed survey that organizes prior results under a common analytic toolkit while explicitly noting necessary adaptations would provide a useful reference for researchers working on non-compact and singular manifolds. By highlighting common microlocal techniques across settings, the paper could help consolidate the literature and guide future work on index theory and spectral invariants in these geometries. The absence of new central theorems means its value lies in clarity of exposition and synthesis rather than in novel derivations.

minor comments (2)

[Abstract and introductory sections] The abstract refers to 'sketched proofs' and 'exposition of the geometric and analytic foundations'; ensure that the corresponding sections supply enough concrete references to the original papers so that readers can locate the full details without ambiguity.
[Geometric foundations] Notation for the various cusp structures (incomplete vs. asymptotically hyperbolic vs. Euclidean) should be introduced with a short comparative table or diagram early in the text to improve readability when differences are later discussed.

Simulated Author's Rebuttal

0 responses · 0 unresolved

We thank the referee for their careful reading of the manuscript and for the positive recommendation to accept. Their summary correctly identifies the scope of the survey, the emphasis on microlocal techniques, and the distinctions between incomplete and complete asymptotic regimes.

Circularity Check

0 steps flagged

No significant circularity in survey of prior results

full rationale

This manuscript is a survey that organizes and sketches existing results on fibred cusp spaces from the literature on spectral geometry, analytic torsion, index theory, and boundary value problems. It describes geometric foundations, microlocal analysis of the resolvent and heat kernel, and proof ideas for theorems already established in prior work, while explicitly noting adaptations and differences between incomplete cusp singularities and complete asymptotically hyperbolic or Euclidean structures. No new central theorem, prediction, or first-principles derivation is asserted whose validity depends on a self-referential step, fitted parameter renamed as output, or load-bearing self-citation chain. The uniformity of the analytic toolkit is presented as an organizing observation rather than an unverified assumption that forces the surveyed conclusions. All claims therefore rest on externally cited and independently verifiable prior results.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The paper is a survey and therefore draws its content from prior literature on microlocal analysis, heat kernels, and index theory on manifolds with singularities; no new free parameters, ad-hoc axioms, or invented entities are introduced in the abstract.

axioms (1)

standard math Standard results from microlocal analysis of resolvents and heat kernels on manifolds with singularities.
The survey relies on these established tools as the foundation for the results it compiles.

pith-pipeline@v0.9.0 · 5643 in / 1265 out tokens · 30692 ms · 2026-05-19T04:19:26.449686+00:00 · methodology

discussion (0)

Lean theorems connected to this paper

Citations machine-checked in the Pith Canon. Every link opens the source theorem in the public Lean library.

IndisputableMonolith/Foundation/RealityFromDistinction.lean reality_from_one_distinction unclear

?

unclear
Relation between the paper passage and the cited Recognition theorem.

We give a survey of analytic and geometric results on fibred cusp spaces... The underlying tools include a careful microlocal analysis of the resolvent and the heat kernel.
IndisputableMonolith/Cost/FunctionalEquation.lean washburn_uniqueness_aczel unclear

?

unclear
Relation between the paper passage and the cited Recognition theorem.

The ϕ-calculus... resolvent and heat kernel construction... analytic torsion and index theory

What do these tags mean?

matches: The paper's claim is directly supported by a theorem in the formal canon.
supports: The theorem supports part of the paper's argument, but the paper may add assumptions or extra steps.
extends: The paper goes beyond the formal theorem; the theorem is a base layer rather than the whole result.
uses: The paper appears to rely on the theorem as machinery.
contradicts: The paper's claim conflicts with a theorem or certificate in the canon.
unclear: Pith found a possible connection, but the passage is too broad, indirect, or ambiguous to say the theorem truly supports the claim.

Reference graph

Works this paper leans on

16 extracted references · 16 canonical work pages · 2 internal anchors

[1]

[AGR23] P

[AGR16] P Albin and J Gell-Redman, The Index of Dirac Operators on Incomplete Edge Spaces , Symmetry, Integrability and Geometry: Methods and Applications (2016). [AGR23] P. Albin and J. Gell-Redman, The index formula for families of Dirac type operators on pseudomanifolds, Journal of Differential Geometry 125 (2023), no. 2, 207–343. [Alb05] P. Albin, A r...

work page 2016
[2]

[APS75] M. F. Atiyah, V. K. Patodi, and I. M. Singer, Spectral asymmetry and Riemannian Geom- etry. 1, Math. Proc. Cambridge Phil. Soc. 77 (1975),

work page 1975
[3]

Albin and F

[AR09] P. Albin and F. Rochon, Families index for manifolds with hyperbolic cusp singularities , International Mathematics Research Notices (2009), 625–297. [AS69] M. F. Atiyah and I. M. Singer, The index of elliptic operators on compact manifolds , Bull. Am. Math. Soc. 69 (1969), 422–433. [BC89] J.-M. Bismut and J. Cheeger, Eta invariants and their adiab...

work page 2009
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Borel, Stable real cohomology of arithmetic groups , Ann

[Bor74] A. Borel, Stable real cohomology of arithmetic groups , Ann. Sci. ´Ecole Norm. Sup. (4) 7 (1974), 235–272 (1975). MR 0387496 [Cal63] A. Calder´ on, Boundary Value Problems for Elliptic Equations , Outlines Joint Sympos. Par- tial Differential Equations (Novosibirsk, 1963), Acad. Sci. USSR Siberian Branch, Moscow, 1963, pp. 303–304. [CDR19] R. J. C...

work page 1974
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Debord, J.-M

[DLR15] C. Debord, J.-M. Lescure, and F. Rochon, Pseudodifferential operators on manifolds with fibred corners, Ann. Inst. Fourier (Grenoble) 65 (2015), no. 4, 1799–1880. MR 3449197 [DR24] P. Dimakis and F. Rochon, Asymptotic geometry at infinity of quiver varieties ,

work page 2015
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Fritzsch, D

[FGS23] K. Fritzsch, D. Grieser, and E. Schrohe, The Calder´ on projector for fibred cusp operators, Journal of Functional Analysis 285 (2023), no. 10, 110–127. [FGS25] , The Dirichlet-Neumann operator for fibred cusp spaces , In preparation,

work page 2023
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Foscolo, M

[FHN21] L. Foscolo, M. Haskins, and J. Nordstr¨ om,Complete noncompact G2-manifolds from asymp- totically conical Calabi-yau 3-folds , Duke Math. J. 170 (2021), no. 15, 3323–3416. [Fre21] D. S. Freed, The Atiyah-Singer index theorem , Bulletin of the American Mathematical So- ciety 58 (2021),

work page 2021
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[Gaf55] M. P. Gaffney, Hilbert space methods in the theory of harmonic integrals , Transactions of the American Mathematical Society 78 (1955), 426–444. [Get86] E. Getzler, A short proof of the local Atiyah-Singer index theorem , Topology 25 (1986), no. 1, 111–117. 33 [GG18] V. Grandjean and D. Grieser, The exponential map at a cuspidal singularity , J. R...

work page internal anchor Pith review Pith/arXiv arXiv doi:10.1515/crelle-2015-0020 1955
[9]

Grieser, Basics of the b-calculus, Approaches to Singular Analysis (Basel) (J.B

[Gri01] D. Grieser, Basics of the b-calculus, Approaches to Singular Analysis (Basel) (J.B. Gil, D. Grieser, and M. Lesch, eds.), Advances in Partial Differential Equations, Birkh¨ auser, 2001, pp. 30–84. [Gro23] M. Gromov, Four Lectures on Scalar Curvature , Perspectives in scalar curvature, World Scientific Publishing Co. Pte. Ltd,

work page 2001
[10]

Gell-Redman and J

[GRS15] J. Gell-Redman and J. Swoboda, Spectral and hodge theory of ‘Witt’ incomplete cusp edge spaces, Commentarii Mathematici Helvetici 94 (2015). [GS15] C. Guillarmou and D. A. Sher, Low energy resolvent for the Hodge Laplacian: applications to Riesz transform, Sobolev estimates, and analytic torsion , Int. Math. Res. Not. IMRN 15 (2015), 6136–6210. MR...

work page 2015
[11]

Grieser, M

[GTV22] D. Grieser, M. Talebi, and B. Vertman, Spectral geometry on manifolds with fibered boundary metrics I: Low energy resolvent, Journal de l’´Ecole polytechnique - Math´ ematiques9 (2022), 959–1019. [HHM04] T. Hausel, E. Hunsicker, and R. Mazzeo, Hodge cohomology of gravitational instantons, Duke Math. J. 122 (2004), no. 3, 485–548. [H¨ or85] L. H¨ o...

work page 2022
[12]

Kottke, An index theorem of Callias type for pseudodifferential operators , Journal of K-theory 8 (2011), no

[Kot11] C. Kottke, An index theorem of Callias type for pseudodifferential operators , Journal of K-theory 8 (2011), no. 3, 387–417. [KR21] C. Kottke and F. Rochon, Quasi-fibered boundary pseudodifferential operators , Preprint, arXiv:2103.16650 [math.DG] (2021),

work page arXiv 2011
[13]

[KR22] , Low energy limit for the resolvent of some fibered boundary operators , Commun. Math. Phys. 390 (2022), no. 1, 231–307 (English). [KR24] , l2-cohomology of quasi-fibered boundary metrics , Inventiones mathematicae 236 (2024), 1–49. [Kro89] P. B. Kronheimer, The construction of ALE spaces as hyper-K¨ ahlerquotients, J. Diff. Geom. 29 (1989), no. 3...

work page 2022
[14]

Lesch and N

[LP96] M. Lesch and N. Peyerimhoff, On index formulas for manifolds with metric horns , Commu- nications in Partial Differential Equations 23 (1996). [LV24] J. O. Lye and B. Vertman, Analytic torsion for fibred boundary metrics and conic degener- ation, International Mathematics Research Notices 2025 (2024). 34 [Maz91] R. Mazzeo, Elliptic theory of differ...

work page 1996
[15]

Mazzeo and R

[MM98] R. Mazzeo and R. B. Melrose, Pseudodifferential operators on manifolds with fibred bound- aries, Asian Journal of Mathematics 2 (1998), 833–866. [Moo99] E. A. Mooers, Heat kernel asymptotics on manifolds with conical singularities , Journal d’Analyse Math´ ematique78 (1999), 1–36. [MV14] R. Mazzeo and B. Vertman, Elliptic theory of differential edg...

work page 1998
[16]

MR 891654 [NT08] S. A. Nazarov and J. Taskinen, On the spectrum of the Steklov problem in a domain with a peak, Vestn. St. Petersbg. Univ., Math. 41 (2008), no. 1, 45–52 (English). [RZ12] F. Rochon and Z. Zhang, Asymptotics of complete K¨ ahler metrics of finite volume on quasiprojective manifolds, Adv. Math. 231 (2012), no. 5, 2892–2952. MR 2970469 [See6...

work page internal anchor Pith review Pith/arXiv arXiv 2008

[1] [1]

[AGR23] P

[AGR16] P Albin and J Gell-Redman, The Index of Dirac Operators on Incomplete Edge Spaces , Symmetry, Integrability and Geometry: Methods and Applications (2016). [AGR23] P. Albin and J. Gell-Redman, The index formula for families of Dirac type operators on pseudomanifolds, Journal of Differential Geometry 125 (2023), no. 2, 207–343. [Alb05] P. Albin, A r...

work page 2016

[2] [2]

[APS75] M. F. Atiyah, V. K. Patodi, and I. M. Singer, Spectral asymmetry and Riemannian Geom- etry. 1, Math. Proc. Cambridge Phil. Soc. 77 (1975),

work page 1975

[3] [3]

Albin and F

[AR09] P. Albin and F. Rochon, Families index for manifolds with hyperbolic cusp singularities , International Mathematics Research Notices (2009), 625–297. [AS69] M. F. Atiyah and I. M. Singer, The index of elliptic operators on compact manifolds , Bull. Am. Math. Soc. 69 (1969), 422–433. [BC89] J.-M. Bismut and J. Cheeger, Eta invariants and their adiab...

work page 2009

[4] [4]

Borel, Stable real cohomology of arithmetic groups , Ann

[Bor74] A. Borel, Stable real cohomology of arithmetic groups , Ann. Sci. ´Ecole Norm. Sup. (4) 7 (1974), 235–272 (1975). MR 0387496 [Cal63] A. Calder´ on, Boundary Value Problems for Elliptic Equations , Outlines Joint Sympos. Par- tial Differential Equations (Novosibirsk, 1963), Acad. Sci. USSR Siberian Branch, Moscow, 1963, pp. 303–304. [CDR19] R. J. C...

work page 1974

[5] [5]

Debord, J.-M

[DLR15] C. Debord, J.-M. Lescure, and F. Rochon, Pseudodifferential operators on manifolds with fibred corners, Ann. Inst. Fourier (Grenoble) 65 (2015), no. 4, 1799–1880. MR 3449197 [DR24] P. Dimakis and F. Rochon, Asymptotic geometry at infinity of quiver varieties ,

work page 2015

[6] [6]

Fritzsch, D

[FGS23] K. Fritzsch, D. Grieser, and E. Schrohe, The Calder´ on projector for fibred cusp operators, Journal of Functional Analysis 285 (2023), no. 10, 110–127. [FGS25] , The Dirichlet-Neumann operator for fibred cusp spaces , In preparation,

work page 2023

[7] [7]

Foscolo, M

[FHN21] L. Foscolo, M. Haskins, and J. Nordstr¨ om,Complete noncompact G2-manifolds from asymp- totically conical Calabi-yau 3-folds , Duke Math. J. 170 (2021), no. 15, 3323–3416. [Fre21] D. S. Freed, The Atiyah-Singer index theorem , Bulletin of the American Mathematical So- ciety 58 (2021),

work page 2021

[8] [8]

[Gaf55] M. P. Gaffney, Hilbert space methods in the theory of harmonic integrals , Transactions of the American Mathematical Society 78 (1955), 426–444. [Get86] E. Getzler, A short proof of the local Atiyah-Singer index theorem , Topology 25 (1986), no. 1, 111–117. 33 [GG18] V. Grandjean and D. Grieser, The exponential map at a cuspidal singularity , J. R...

work page internal anchor Pith review Pith/arXiv arXiv doi:10.1515/crelle-2015-0020 1955

[9] [9]

Grieser, Basics of the b-calculus, Approaches to Singular Analysis (Basel) (J.B

[Gri01] D. Grieser, Basics of the b-calculus, Approaches to Singular Analysis (Basel) (J.B. Gil, D. Grieser, and M. Lesch, eds.), Advances in Partial Differential Equations, Birkh¨ auser, 2001, pp. 30–84. [Gro23] M. Gromov, Four Lectures on Scalar Curvature , Perspectives in scalar curvature, World Scientific Publishing Co. Pte. Ltd,

work page 2001

[10] [10]

Gell-Redman and J

[GRS15] J. Gell-Redman and J. Swoboda, Spectral and hodge theory of ‘Witt’ incomplete cusp edge spaces, Commentarii Mathematici Helvetici 94 (2015). [GS15] C. Guillarmou and D. A. Sher, Low energy resolvent for the Hodge Laplacian: applications to Riesz transform, Sobolev estimates, and analytic torsion , Int. Math. Res. Not. IMRN 15 (2015), 6136–6210. MR...

work page 2015

[11] [11]

Grieser, M

[GTV22] D. Grieser, M. Talebi, and B. Vertman, Spectral geometry on manifolds with fibered boundary metrics I: Low energy resolvent, Journal de l’´Ecole polytechnique - Math´ ematiques9 (2022), 959–1019. [HHM04] T. Hausel, E. Hunsicker, and R. Mazzeo, Hodge cohomology of gravitational instantons, Duke Math. J. 122 (2004), no. 3, 485–548. [H¨ or85] L. H¨ o...

work page 2022

[12] [12]

Kottke, An index theorem of Callias type for pseudodifferential operators , Journal of K-theory 8 (2011), no

[Kot11] C. Kottke, An index theorem of Callias type for pseudodifferential operators , Journal of K-theory 8 (2011), no. 3, 387–417. [KR21] C. Kottke and F. Rochon, Quasi-fibered boundary pseudodifferential operators , Preprint, arXiv:2103.16650 [math.DG] (2021),

work page arXiv 2011

[13] [13]

[KR22] , Low energy limit for the resolvent of some fibered boundary operators , Commun. Math. Phys. 390 (2022), no. 1, 231–307 (English). [KR24] , l2-cohomology of quasi-fibered boundary metrics , Inventiones mathematicae 236 (2024), 1–49. [Kro89] P. B. Kronheimer, The construction of ALE spaces as hyper-K¨ ahlerquotients, J. Diff. Geom. 29 (1989), no. 3...

work page 2022

[14] [14]

Lesch and N

[LP96] M. Lesch and N. Peyerimhoff, On index formulas for manifolds with metric horns , Commu- nications in Partial Differential Equations 23 (1996). [LV24] J. O. Lye and B. Vertman, Analytic torsion for fibred boundary metrics and conic degener- ation, International Mathematics Research Notices 2025 (2024). 34 [Maz91] R. Mazzeo, Elliptic theory of differ...

work page 1996

[15] [15]

Mazzeo and R

[MM98] R. Mazzeo and R. B. Melrose, Pseudodifferential operators on manifolds with fibred bound- aries, Asian Journal of Mathematics 2 (1998), 833–866. [Moo99] E. A. Mooers, Heat kernel asymptotics on manifolds with conical singularities , Journal d’Analyse Math´ ematique78 (1999), 1–36. [MV14] R. Mazzeo and B. Vertman, Elliptic theory of differential edg...

work page 1998

[16] [16]

MR 891654 [NT08] S. A. Nazarov and J. Taskinen, On the spectrum of the Steklov problem in a domain with a peak, Vestn. St. Petersbg. Univ., Math. 41 (2008), no. 1, 45–52 (English). [RZ12] F. Rochon and Z. Zhang, Asymptotics of complete K¨ ahler metrics of finite volume on quasiprojective manifolds, Adv. Math. 231 (2012), no. 5, 2892–2952. MR 2970469 [See6...

work page internal anchor Pith review Pith/arXiv arXiv 2008