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Metric Geometry

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Total of 90 entries : 1-50 51-90
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Wed, 14 Oct 2026 (showing 44 of 44 entries )

[1] arXiv:2610.18770 [pdf, html, other]
Title: On plank coverings of cube annuli
Gergely Ambrus, Matthew Corbo, Dakota Nobuyuki Goto, Desmond Leitz, Kai Mawhinney
Comments: 21 pages
Subjects: Metric Geometry (math.MG)
[2] arXiv:2610.18351 [pdf, html, other]
Title: An explicit dimension-free isoperimetric plateau in the cube
Lei Yu
Comments: 23 pages
Subjects: Metric Geometry (math.MG)
[3] arXiv:2610.18268 [pdf, html, other]
Title: Radon Transforms of Projection Functions and Aleksandrov-Fenchel Inequalities
Leo Brauner, Oscar Ortega-Moreno, Franz E. Schuster
Comments: 21 pages
Subjects: Metric Geometry (math.MG); Functional Analysis (math.FA)
[4] arXiv:2610.18132 [pdf, html, other]
Title: Excess inertia of finite metric spaces
Kiyonori Gomi
Comments: LaTeX 2e, 28 pages
Subjects: Metric Geometry (math.MG)
[5] arXiv:2610.17909 [pdf, html, other]
Title: Geometry and barycenters in large $\CAT(κ)$ spaces
Yassine Boukhateb, Victor-Emmanuel Brunel, Austin J. Stromme
Subjects: Metric Geometry (math.MG); Statistics Theory (math.ST)
[6] arXiv:2610.17863 [pdf, html, other]
Title: Non-smooth sub-Riemannian manifolds with non-integer dimension and a Poincaré inequality
Sylvester Eriksson-Bique, Enrico Le Donne
Comments: 42 pages, comments welcome
Subjects: Metric Geometry (math.MG)
[7] arXiv:2610.17400 [pdf, html, other]
Title: Steiner Minimal Trees in the Gromov--Hausdorff Space and in Gromov--Hausdorff Clouds
I. N. Mikhailov
Comments: 16 pages, 3 figures, working paper
Subjects: Metric Geometry (math.MG)
[8] arXiv:2610.17004 [pdf, html, other]
Title: Intrinsic Rigidity of Bar-and-Joint Frameworks on Riemannian Manifolds
Matthias Adrian-Himmelmann
Comments: 28 pages plus 8 pages appendix, 7 figures
Subjects: Metric Geometry (math.MG); Differential Geometry (math.DG)
[9] arXiv:2610.16997 [pdf, html, other]
Title: A new family of constant width bodies obtained from Reuleaux polyhedra
Marcela G. Mercado-Flores, Edgardo Roldán-Pensado
Subjects: Metric Geometry (math.MG)
[10] arXiv:2610.16904 [pdf, html, other]
Title: Exponential profiles for the intrinsic volumes of Orlicz balls
Mykyta Sadok
Comments: 27 pages;
Subjects: Metric Geometry (math.MG); Probability (math.PR)
[11] arXiv:2610.15851 [pdf, html, other]
Title: Unrectifiable surfaces with intrinsic regularity in Carnot groups
Valentino Magnani, Jeremy Mirmina
Comments: 29 pages
Subjects: Metric Geometry (math.MG)
[12] arXiv:2610.14380 [pdf, other]
Title: Lattices with Large Kissing Number from Local Density
Huck Bennett, Minki Hhan, Zihan Li, Noah Stephens-Davidowitz
Subjects: Metric Geometry (math.MG); Number Theory (math.NT)
[13] arXiv:2610.14236 [pdf, html, other]
Title: Quasiconformal uniformization and extension for planar trees
Fotis Ioannidis Vyron Vellis
Comments: 67 pages, 14 figures
Subjects: Metric Geometry (math.MG)
[14] arXiv:2610.14055 [pdf, html, other]
Title: Upper bounds for Jung constants of $\ell_1^d$
Xiao Li
Subjects: Metric Geometry (math.MG); Combinatorics (math.CO)
[15] arXiv:2610.14047 [pdf, html, other]
Title: Maximal volumes of pyramids in the unit cube
Nikolai Nikolov
Subjects: Metric Geometry (math.MG)
[16] arXiv:2610.14037 [pdf, html, other]
Title: Sharp Antipode-Neighbor Bounds in Every Dimension
Samuel Korsky
Subjects: Metric Geometry (math.MG); Combinatorics (math.CO)
[17] arXiv:2610.14032 [pdf, html, other]
Title: Polygons and coplanar points on submanifolds of codimension 2
Sohail (Neel)Sarkar
Comments: 11 pages
Subjects: Metric Geometry (math.MG); Combinatorics (math.CO); Differential Geometry (math.DG)
[18] arXiv:2610.13983 [pdf, html, other]
Title: Equilateral sets in $\ell_p^n$ beyond $n+1$: Linear excess and dimension cost
Logan R. Chalmers, Aran S. Ziegler
Comments: 7 pages
Subjects: Metric Geometry (math.MG); Combinatorics (math.CO)
[19] arXiv:2610.13978 [pdf, other]
Title: An Improved Lower Bound for Packing 203 Equal Spheres in a Unit Cube
Peng Lu
Comments: Code and data: this https URL
Subjects: Metric Geometry (math.MG)
[20] arXiv:2610.13975 [pdf, html, other]
Title: The rhombic dodecahedral conjecture
Annalisa Cesaroni, Matteo Novaga
Comments: 17 pages
Subjects: Metric Geometry (math.MG); Analysis of PDEs (math.AP); Combinatorics (math.CO)
[21] arXiv:2610.13972 [pdf, html, other]
Title: Insertion and expansion of cylinders around the unit ball
Ivan Matić, Radoš Radoičić, Andreas Spomer
Subjects: Metric Geometry (math.MG); Combinatorics (math.CO)
[22] arXiv:2610.13965 [pdf, html, other]
Title: Jensen's inequality on parity classes of jump M-convex functions
Xinyue Liu
Comments: 12 pages
Subjects: Metric Geometry (math.MG); Combinatorics (math.CO)
[23] arXiv:2610.13964 [pdf, html, other]
Title: A 0.41275 lower bound for the three-dimensional Blaschke-Lebesgue problem
Yunjiang Jiang
Subjects: Metric Geometry (math.MG); Computational Geometry (cs.CG)
[24] arXiv:2610.13962 [pdf, html, other]
Title: A Power-Diagram Upper Bound for Twenty-Six Variable-Radius Disks in a Square
Ayush Agarwal
Comments: 15 pages, 1 figure; exact rational feasibility and upper-bound verification scripts and data included as ancillary source files
Subjects: Metric Geometry (math.MG)
[25] arXiv:2610.13961 [pdf, html, other]
Title: Necessary and Sufficient Criteria for the Realizability of Kaleidocycles Composed of Six Congruent Isosceles Tetrahedra
Herbert Kociemba
Comments: Supplementary Mathematica notebook containing computational details is included
Subjects: Metric Geometry (math.MG)
[26] arXiv:2610.13958 [pdf, html, other]
Title: Thirteen Results in Magnitude Theory
Venkata Siddharth Pendyala
Comments: 31 pages; comments or concerns are very much appreciated
Subjects: Metric Geometry (math.MG)
[27] arXiv:2610.13957 [pdf, html, other]
Title: $L_p$-Integral Affine Surface Area-Variational Capacity Inequalities
Yibin Feng, Ding Zhang
Subjects: Metric Geometry (math.MG)
[28] arXiv:2610.13955 [pdf, html, other]
Title: Certified Geometry and Admissible Motion of Gerver's Sofa
Dawid Trela
Comments: 22 pages. Includes a deterministic exact-rational companion verifier and independent 4-dimensional and 22-dimensional Krawczyk certificates
Subjects: Metric Geometry (math.MG); Computational Geometry (cs.CG)
[29] arXiv:2610.13953 [pdf, html, other]
Title: On the Reverse Projection Inequality
Yibin Feng, Shengnan Hu, Weiru Liu, Lei Xu
Subjects: Metric Geometry (math.MG); Differential Geometry (math.DG)
[30] arXiv:2610.13952 [pdf, html, other]
Title: Breaking the Fourth Wall: The Planar Centroid Banach--Mazur Diameter Is Strictly Less than $4$
Scott Duke Kominers
Comments: 11 pages, 2 figures
Subjects: Metric Geometry (math.MG)
[31] arXiv:2610.13950 [pdf, html, other]
Title: Platonic geodesic trees in the $K-$Space
Anastasios N. Zachos
Comments: 9 pages
Subjects: Metric Geometry (math.MG); Optimization and Control (math.OC)
[32] arXiv:2610.17270 (cross-list from math.CO) [pdf, html, other]
Title: Integer decomposition property of three-dimensional smooth polytopes: a shorter proof
Juliana Curtis, Gaku Liu
Comments: 7 pages
Subjects: Combinatorics (math.CO); Algebraic Geometry (math.AG); Metric Geometry (math.MG)
[33] arXiv:2610.17194 (cross-list from math.FA) [pdf, html, other]
Title: Absolutely minimising Lipschitz extensions between Hilbert spaces
Krzysztof J. Ciosmak
Comments: 25 pages, comments are welcome
Subjects: Functional Analysis (math.FA); Metric Geometry (math.MG)
[34] arXiv:2610.16740 (cross-list from math.PR) [pdf, html, other]
Title: Revisiting the Bobkov-Chistyakov-Götze theorem on approximately Gaussian marginals
Boaz Klartag
Comments: 10 pages. The use of AI is described in the acknowledgements
Subjects: Probability (math.PR); Metric Geometry (math.MG)
[35] arXiv:2610.15889 (cross-list from math.FA) [pdf, html, other]
Title: The $p$-Bures-Wasserstein distance via $3\times3$ block matrices (with application to $p$-Bures-Wasserstein barycenters)
Suvrit Sra
Comments: 20 pages; 4 appendices; one synthetic experiment included
Subjects: Functional Analysis (math.FA); Metric Geometry (math.MG); Optimization and Control (math.OC)
[36] arXiv:2610.15716 (cross-list from math.PR) [pdf, html, other]
Title: Sharp Rogers--Shephard Inequalities for Rényi Entropy
Bang-Xian Han, Guoqing Zhan, Chiyu Zhou, Zhuo-Nan Zhu
Comments: 29 pages; comments are welcome!
Subjects: Probability (math.PR); Information Theory (cs.IT); Metric Geometry (math.MG)
[37] arXiv:2610.15424 (cross-list from math.CO) [pdf, html, other]
Title: Every n points in the plane contain (m1 + o(1)) n points with no unit distance
Shisheng Li, Yong Su
Subjects: Combinatorics (math.CO); Metric Geometry (math.MG)
[38] arXiv:2610.15265 (cross-list from cs.CR) [pdf, html, other]
Title: Asymptotics of Random-Lattice Enumeration: Beyond HKZ via Dense Sublattices
Thijs Laarhoven
Comments: 27 pages, 4 figures, 2 tables
Subjects: Cryptography and Security (cs.CR); Combinatorics (math.CO); Metric Geometry (math.MG)
[39] arXiv:2610.14275 (cross-list from math.RT) [pdf, html, other]
Title: Polytopal invariance for Lusztig's $q$-weight multiplicities
Nicolás Libedinsky
Comments: 23 pages, 3 figures, comments welcome
Subjects: Representation Theory (math.RT); Combinatorics (math.CO); Metric Geometry (math.MG)
[40] arXiv:2610.14160 (cross-list from math.CA) [pdf, other]
Title: Uniformly Bounded Orthonormal Bases of Homogeneous Polynomials on the Complex Sphere
Felipe Gonçalves, João P. Ferreira, Maksym Radziwiłł
Comments: 38 pages
Subjects: Classical Analysis and ODEs (math.CA); Metric Geometry (math.MG); Number Theory (math.NT)
[41] arXiv:2610.14051 (cross-list from cs.CG) [pdf, html, other]
Title: New certified lower bounds for the moving sofa problem in a three-dimensional snaky corridor
Yuzhe Tang
Subjects: Computational Geometry (cs.CG); Metric Geometry (math.MG)
[42] arXiv:2610.14050 (cross-list from cs.CG) [pdf, html, other]
Title: An upper bound for the three-dimensional moving sofa problem in a snaky corridor
Yuzhe Tang
Comments: 18 pages. Code, machine-verification scripts and resumable certificates at this https URL
Subjects: Computational Geometry (cs.CG); Metric Geometry (math.MG)
[43] arXiv:2610.13986 (cross-list from math.HO) [pdf, html, other]
Title: Triangles and quadrilaterals suffice
Mu-Tsun Tsai
Subjects: History and Overview (math.HO); Metric Geometry (math.MG)
[44] arXiv:2610.13954 (cross-list from math.DG) [pdf, html, other]
Title: Bisectors in the Heisenberg group II
Gaoshun Gou, Joonhyung Kim, Ioannis D. Platis, Li-Jie Sun
Subjects: Differential Geometry (math.DG); Group Theory (math.GR); Metric Geometry (math.MG)

Mon, 12 Oct 2026 (showing 5 of 5 entries )

[45] arXiv:2610.13475 [pdf, html, other]
Title: Each simplex in $\mathbb{R}^4$ has a point with at least $14$ emanating normals to its boundary
Ivan Nasonov, Gaiane Panina
Subjects: Metric Geometry (math.MG)
[46] arXiv:2610.12626 [pdf, html, other]
Title: Pointed Gromov-Hausdorff Distance between $l^p$-Wedge Sums and Isometric Embeddings of $l^\infty$
Emin Abdullaev
Comments: 18 pages
Subjects: Metric Geometry (math.MG)
[47] arXiv:2610.13885 (cross-list from cond-mat.mtrl-sci) [pdf, html, other]
Title: Necessary conditions for benchmarking next-generation AI in materials discovery
Daniel E Widdowson, Tatiana V Kurlina, Olga D Anosova, Vitaliy A Kurlin
Comments: 44 pages, 16 figures
Subjects: Materials Science (cond-mat.mtrl-sci); Metric Geometry (math.MG)
[48] arXiv:2610.13055 (cross-list from math.GR) [pdf, html, other]
Title: Cohomology and multiplicative gaps for quasi-isometries of nilpotent groups
Mayukh Mukherjee, Soumyadeb Samanta, Soumyadip Thandar
Comments: 34 pages. This is split off from the authors' previous submission arXiv:2512.06753. Comments are most welcome!
Subjects: Group Theory (math.GR); Differential Geometry (math.DG); Metric Geometry (math.MG)
[49] arXiv:2610.12619 (cross-list from math.NT) [pdf, html, other]
Title: A cyclotomic gluing construction for lattice sphere packings
Nihar Gargava, Matthias Gröbner, Michael Simkin
Comments: 39 pages, 3 figures
Subjects: Number Theory (math.NT); Metric Geometry (math.MG)

Fri, 9 Oct 2026 (showing first 1 of 18 entries )

[50] arXiv:2610.12029 [pdf, html, other]
Title: Embedding large subsets of Wasserstein spaces into Banach spaces
Cyril Letrouit, Quentin Mérigot
Subjects: Metric Geometry (math.MG)
Total of 90 entries : 1-50 51-90
Showing up to 50 entries per page: fewer | more | all