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307 papers in math.MG · page 6
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Morse theory equips distance critical points with quadratic and piecewise-linear indices
Morse theory of Euclidean distance functions from algebraic hypersurfaces
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Cotangent orbits embed infinite-dimensional space under spectral metric
Spectrally-large scale geometry in cotangent bundles
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Integer-distance point sets remain finite outside Euclidean space
Non-Euclidean Erd\H{o}s-Anning Theorems
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Axioms turn automata into generators of self-similar topologies
Elementary fractal geometry. 4. Automata-generated topological spaces
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Outer billiards on most regular polygons have aperiodic points
Aperiodic points for outer billiards
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Random disc-polygon area obeys quantitative CLT
A central limit theorem for random disc-polygons in smooth convex discs
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Quasi-isometry to planar graphs forces groups to be virtual free products
Accessibility, planar graphs, and quasi-isometries
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Log gradient bounds proved for elliptic equations on RCD spaces
Gradient estimate and Universal bounds for semilinear elliptic equations on RCD$^*$(K,N) metric measure spaces
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Gluing preserves CD(K,N) bounds under boundary matching
Glued spaces and lower Ricci curvature bounds
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Floppy graph metrics extend to full metrics when missing edges are countable
Game extensions of floppy graph metrics
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Banakh spaces realize any distance set without embedding in the reals
Banakh spaces and their geometry
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Complete invariants classify atomic clouds and separate their mirrors in polynomial time
Complete invariants of atomic clouds under rigid motion with Lipschitz continuous metrics in a polynomial time
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Quasi-isometries of horospherical products stay close to product maps
Geometric rigidity of quasi-isometries in horospherical products
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Constricting element forces smaller relative growth in quasi-convex subgroups
Growth of quasi-convex subgroups in groups with a constricting element
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Free boundaries form (N-1)-manifolds on RCD spaces except near low-dim sets
One-phase Free Boundary Problems on RCD Metric Measure Spaces
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Lower bounds match upper bounds on disc-polygon variances
Variance bounds for disc-polygons
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Random disc-polygons match classical polygon asymptotics
On random disc-polygons in a disc-polygon
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Dyadic cubes link any points with three comparable cubes
Systems of Dyadic Cubes of Complete, Doubling, Uniformly Perfect Metric Spaces without Detours
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Log-concave measures obey Brunn-Minkowski with exponent n^{-4-o(1)}
A universal bound in the dimensional Brunn-Minkowski inequality for log-concave measures
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d-dimensional grids allow ~n^{d-1} d^{1/(2d)} non-collinear points
On the general no-three-in-line problem
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Blowup polynomial of any metric space is multi-affine and real-stable
The blowup-polynomial of a metric space: connections to stable polynomials, graphs and their distance spectra
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Conformal dimension equals critical p-energy exponent on graphs
Ahlfors Regular Conformal Dimension of Metrics on Infinite Graphs and Spectral Dimension of the Associated Random Walks
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Symmetric cap bodies of balls need at most six directions
On the illumination of centrally symmetric cap bodies in small dimensions
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Diagonal cube section volumes increase strictly with dimension
Central diagonal sections of the $n$-cube
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Tangent cone of medial axis relates to closest-point medial axis
The tangent cone, the dimension and the frontier of a medial axis
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Superquadracity links sets to their medial axis closures
On the singular points approached by the medial axis
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Unit distances in R^k at least C sqrt(k) n
On the Erd\H{o}s distance problem
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Stability strengthens simplex bounds on mean width
Strengthened inequalities for the mean width and the $\ell$-norm
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One criterion decides amenability for full groups of ample groupoids
Representation theory of topological full groups of \'etale groupoids and paradoxicality
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Finite perimeter sets decompose into indecomposables in metric spaces
Indecomposable sets of finite perimeter in doubling metric measure spaces
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Simple polygonal arcs have at most two support line pairs per angle
How support lines touch an arc
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Asymptotic filtered colimits preserve coarse invariants
Asymptotic Filtered Colimits
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Explicit formula for Gromov-Hausdorff distance between simplex and 2-distance space
The Gromov--Hausdorff Distance between Simplexes and Two-Distance Spaces
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Transference bound tightened to 0.1275n
An improved constant in Banaszczyk's transference theorem
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Only univariate polynomials have locally bi-Lipschitz trivial values
A note on the local Lipschitz triviality of values of complex polynomial functions
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Favourite distances in 3D reach n²/4 + 5n/2 + O(1)
Favourite distances in 3-space
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Any real set contains a full subset avoiding rational distances
A note on sets avoiding rational distances
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Table lists best-known packings in complex projective space
Game of Sloanes: Best known packings in complex projective space
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30° sector covers every unit arc
Wetzel's sector covers unit arcs
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A∞ on curves yields L^p Alberti representations
Quantitative Alberti representations in spaces of bounded geometry
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New proof shows simple arcs obey the Λ-property
The $\Lambda$-property of a simple arc
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Subharmonic volume average bounded by 2n^{3/2} times surface average
Improved Bounds for Hermite-Hadamard Inequalities in Higher Dimensions
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Relaxation is tight for real rank-2 perturbed identities
Optimally Perturbed Identity Matrices of Rank 2
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Any n unit vectors admit v with sum 1/<ui,v>^2 <= n^2
Analytic and Probabilistic Problems in Discrete Geometry
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Upper box dimension d yields α-Hölder curve for any α < 1/d
Box-counting by H\"older's traveling salesman
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Inclusion of bornological spaces yields equivalence of coarse spectra
Generalized bornological coarse spaces and coarse motivic spectra
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New formula for Gromov-Hausdorff distance to simplexes
The Gromov-Hausdorff Distances between Simplexes and Ultrametric Spaces
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Higson corona equals quotient of coarse ultrafilters
Coarse Homotopy on metric Spaces and their Corona
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Unique shortest curve in U(n) only when spectrum is two-point symmetric
Minimal curves in U(n) and Gl(n)+ with respect to the spectral and the trace norms
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Block-permuted inductive means converge to matrix least square mean
New deterministic approaches to the least square mean