Metric Geometry

Authors and titles for July 2022

[1] arXiv:2207.00333 [pdf, other]

Title: A framework for stereo vision via optimal transport

Mattia Galeotti, Alessandro Sarti, Giovanna Citti

Comments: 18 pages, 12 figures

Subjects: Metric Geometry (math.MG); Optimization and Control (math.OC)

[2] arXiv:2207.00482 [pdf, html, other]

Title: The Cheeger problem in abstract measure spaces

Valentina Franceschi, Andrea Pinamonti, Giorgio Saracco, Giorgio Stefani

Comments: 52 pages

Journal-ref: J. London Math. Soc. 119(1):e12840, 2024

Subjects: Metric Geometry (math.MG); Functional Analysis (math.FA)

[3] arXiv:2207.01495 [pdf, other]

Title: Inclusion properties of the triangular ratio metric balls

Oona Rainio

Comments: 23 pages, 5 figures

Subjects: Metric Geometry (math.MG)

[4] arXiv:2207.02557 [pdf, other]

Title: Periodic geodesics in singular spaces

Panos Papasoglu, Eric Swenson

Comments: 7 pages

Subjects: Metric Geometry (math.MG)

[5] arXiv:2207.02949 [pdf, other]

Title: Sobolev spaces and Poincar\'e inequalities on the Vicsek fractal

Fabrice Baudoin, Li Chen

Comments: V2: Accepted for publication in Ann. Fenn. Math

Subjects: Metric Geometry (math.MG); Classical Analysis and ODEs (math.CA); Functional Analysis (math.FA)

[6] arXiv:2207.03013 [pdf, other]

Title: The Riesz tranform on intrinsic Lipschitz graphs in the Heisenberg group

Vasileios Chousionis, Sean Li, Robert Young

Subjects: Metric Geometry (math.MG); Classical Analysis and ODEs (math.CA)

[7] arXiv:2207.03043 [pdf, other]

Title: Stability of the isodiametric problem on the sphere and in the hyperbolic space

Károly J. Böröczky, Ádám Sagmeister

Subjects: Metric Geometry (math.MG)

[8] arXiv:2207.03423 [pdf, html, other]

Title: Rigidities of Isoperimetric inequality under nonnegative Ricci curvature

Fabio Cavalletti, Davide Manini

Comments: 49 pages; minor corrections; add Remark 1.6

Subjects: Metric Geometry (math.MG)

[9] arXiv:2207.03614 [pdf, other]

Title: Approximate Carath\'eodory bounds via Discrepancy Theory

Victor Reis, Thomas Rothvoss

Comments: 16 pages

Subjects: Metric Geometry (math.MG); Data Structures and Algorithms (cs.DS)

[10] arXiv:2207.03943 [pdf, other]

Title: A Geometric Condition for Uniqueness of Fr\'echet Means of Persistence Diagrams

Yueqi Cao, Anthea Monod

Comments: 15 pages, 3 figures

Subjects: Metric Geometry (math.MG); Methodology (stat.ME)

[11] arXiv:2207.04486 [pdf, other]

Title: The intrinsic Hopf-Lax semigroup vs. The intrinsic slope

Daniela Di Donato

Subjects: Metric Geometry (math.MG); Differential Geometry (math.DG)

[12] arXiv:2207.05416 [pdf, other]

Title: Convergence properties of symmetrization processes

Jacopo Ulivelli

Subjects: Metric Geometry (math.MG); Probability (math.PR)

[13] arXiv:2207.06375 [pdf, other]

Title: Affine Fractional Sobolev and Isoperimetric Inequalities

Julián Haddad, Monika Ludwig

Subjects: Metric Geometry (math.MG); Functional Analysis (math.FA)

[14] arXiv:2207.06913 [pdf, other]

Title: The work of Maryna Viazovska

Henry Cohn

Comments: Fields Medal laudatio, 24 pages, 8 figures

Subjects: Metric Geometry (math.MG); History and Overview (math.HO)

[15] arXiv:2207.06923 [pdf, other]

Title: Integral Identities for the boundary of a convex body

Tatiana Moseeva

Comments: 12 pages

Subjects: Metric Geometry (math.MG); Probability (math.PR)

[16] arXiv:2207.07377 [pdf, other]

Title: The limit of $L_p$ Voronoi diagrams as $p \rightarrow 0$ is the bounding-box-area Voronoi diagram

Herman Haverkort, Rolf Klein

Comments: 15 pages, 13 figures

Subjects: Metric Geometry (math.MG); Computational Geometry (cs.CG)

[17] arXiv:2207.07865 [pdf, other]

Title: A new perspective on taxicab conic sections

Emily Frost, Dylan Helliwell, Suki Shergill

Comments: 42 pages, 17 figures, submitted to The Art of Discrete and Applied Mathematics

Subjects: Metric Geometry (math.MG)

[18] arXiv:2207.08458 [pdf, other]

Title: Shrinking target for $C^1$ weakly conformal IFS with overlaps

Edouard Daviaud (UPEC FST)

Comments: arXiv admin note: text overlap with arXiv:2204.01302

Subjects: Metric Geometry (math.MG)

[19] arXiv:2207.08477 [pdf, other]

Title: Affine Subspace Concentration Conditions for Centered Polytopes

Ansgar Freyer, Martin Henk, Christian Kipp

Subjects: Metric Geometry (math.MG)

[20] arXiv:2207.08763 [pdf, other]

Title: Universal Rigidity of Ladders on the line

Bryan Chen, Robert Connelly, Steven J. Gortler, Anthony Nixon, Louis Theran

Subjects: Metric Geometry (math.MG); Combinatorics (math.CO)

[21] arXiv:2207.08959 [pdf, other]

Title: Densest plane group packings of regular polygons

Miloslav Torda, John Y. Goulermas, Vitaliy Kurlin, Graeme M. Day

Journal-ref: Phys. Rev. E 106, 054603 (2022)

Subjects: Metric Geometry (math.MG); Soft Condensed Matter (cond-mat.soft); Statistical Mechanics (cond-mat.stat-mech); Mathematical Physics (math-ph)

[22] arXiv:2207.09030 [pdf, other]

Title: On the lower bound for kissing numbers of $\ell_p$-spheres in high dimensions

Chengfei Xie, Gennian Ge

Comments: 15 pages, 4 figures; any comments are welcome

Subjects: Metric Geometry (math.MG); Combinatorics (math.CO)

[23] arXiv:2207.09552 [pdf, other]

Title: New estimates for $d_{2,1}$ and $d_{3,2}$

Arkadiy Aliev

Comments: 9 pages, 2 figures

Subjects: Metric Geometry (math.MG)

[24] arXiv:2207.09758 [pdf, other]

Title: Equivariant Endomorphisms of Convex Functions

Georg C. Hofstätter, Jonas Knoerr

Comments: 33 pages

Subjects: Metric Geometry (math.MG); Functional Analysis (math.FA)

[25] arXiv:2207.10159 [pdf, other]

Title: On bi-Lipschitz isomorphisms of self-similar Jordan arcs

Ilya Galai, Andrei Tetenov

Subjects: Metric Geometry (math.MG)

[26] arXiv:2207.11305 [pdf, other]

Title: Vertical versus horizontal inequalities on simply connected nilpotent Lie groups and groups of polynomial growth

Seung-Yeon Ryoo

Comments: 56 pages

Subjects: Metric Geometry (math.MG); Classical Analysis and ODEs (math.CA); Functional Analysis (math.FA); Group Theory (math.GR)

[27] arXiv:2207.11866 [pdf, other]

Title: On Carrasco Piaggio's theorem characterizing quasisymmetric maps from compact doubling spaces to Ahlfors regular spaces

Nageswari Shanmugalingam

Comments: 23 pages

Subjects: Metric Geometry (math.MG); Analysis of PDEs (math.AP)

[28] arXiv:2207.12191 [pdf, html, other]

Title: Korevaar-Schoen-Sobolev spaces and critical exponents in metric measure spaces

Fabrice Baudoin

Comments: Previous version of the manuscript was used as Lecture Notes for the mini course hold at Texas A&M during the workshop Geometry and Analysis on Nonsmooth Spaces, August 8-12 2022. v6: Final version to appear in Ann. Fenn

Subjects: Metric Geometry (math.MG); Functional Analysis (math.FA)

[29] arXiv:2207.12347 [pdf, other]

Title: Degrees of maps and multiscale geometry

Aleksandr Berdnikov, Larry Guth, Fedor Manin

Comments: 49 pages, 3 figures. Theorem C was proved incorrectly in v1; v2 corrects the proof and generalizes the theorem. Other corrections and clarifications are given in response to a referee report

Journal-ref: Forum Math. Pi, vol. 12 (2024) art. e2

Subjects: Metric Geometry (math.MG); Algebraic Topology (math.AT); Differential Geometry (math.DG)

[30] arXiv:2207.12765 [pdf, other]

Title: On comeager sets of metrics whose ranges are disconnected

Yoshito Ishiki

Comments: 13 pages. This paper is published in Topology and its Applications vol.327 (2023), 108442

Journal-ref: Topology and its Applications vol.327 (2023), 108442

Subjects: Metric Geometry (math.MG); General Topology (math.GN)

[31] arXiv:2207.12905 [pdf, other]

Title: Extending proper metrics

Yoshito Ishiki

Comments: 15 pages. This paper is published in Topology and its Applications

Journal-ref: Topology and its Applications. (2022) No. 108387

Subjects: Metric Geometry (math.MG); General Topology (math.GN)

[32] arXiv:2207.13023 [pdf, other]

Title: On Bi-Lipschitz classification of fractal cubes possessing one-point intersection property

A.Tetenov, M.Chanchieva, D.Drozdov, D.Rahmanov, V.Safonova, I.Udin, A. Vetrova

Comments: The work was supported by the Ministry of Science and Higher Education of Russia (agreement No. 075-02-2022-884)

Subjects: Metric Geometry (math.MG)

[33] arXiv:2207.13294 [pdf, other]

Title: A characterization of the ellipsoid by planar grazes

Ivan Gonzalez Garcia, Jesus Jeronimo Castro, Diana Janett Verdusco Hernandez, Efren Morales Amaya

Subjects: Metric Geometry (math.MG)

[34] arXiv:2207.13672 [pdf, other]

Title: Boundaries for geodesic spaces

Jerzy Dydak, Hussain Rashed

Comments: 15 pages

Subjects: Metric Geometry (math.MG); General Topology (math.GN); Geometric Topology (math.GT)

[35] arXiv:2207.13745 [pdf, other]

Title: On regularity of maximal distance minimizers in Euclidean Space

Alexey Gordeev, Yana Teplitskaya

Comments: This work is the advanced version of the work arXiv:1910.07630,2019

Subjects: Metric Geometry (math.MG)

[36] arXiv:2207.14021 [pdf, other]

Title: Groups of convex bodies

Richard Hepworth

Comments: 19 pages

Subjects: Metric Geometry (math.MG)

[37] arXiv:2207.14127 [pdf, html, other]

Title: Hyperbolic models for CAT(0) spaces

Harry Petyt, Davide Spriano, Abdul Zalloum

Comments: 54 pages. v4: Accepted version. v3: Small corrections and clarifications, added an extra figure. v2: Added Section 9, unifying the family of models from v1 into a single space

Subjects: Metric Geometry (math.MG); Group Theory (math.GR)

[38] arXiv:2207.14179 [pdf, other]

Title: The density of planar sets avoiding unit distances

Gergely Ambrus, Adrián Csiszárik, Máté Matolcsi, Dániel Varga, Pál Zsámboki

Comments: 24 pages, 6 figures. Final version, to appear in Mathematical Programming

Subjects: Metric Geometry (math.MG)

[39] arXiv:2207.14369 [pdf, other]

Title: Equilibrium stresses and rigidity for infinite tensegrities and frameworks

Stephen Power

Comments: Journal accepted version, to appear in the Journal of Mathematical Analysis and Applications. 19 pages, 8 figures. More detail and examples given. The implication "BPS implies BSR (boundedly smoothly rigid)" has been strengthened to "BPS implies DCR (directedly continuously rigid)"

Subjects: Metric Geometry (math.MG)

[40] arXiv:2207.14641 [pdf, other]

Title: Quasiconformal Mappings and Curvatures on Metric Measure Spaces

Jialong Deng

Comments: Added the definition of RCD spaces. Accepted version

Subjects: Metric Geometry (math.MG); Complex Variables (math.CV)

[41] arXiv:2207.00963 (cross-list from math.FA) [pdf, other]

Title: A metric fixed point theorem and some of its applications

Anders Karlsson

Comments: 22 pages

Subjects: Functional Analysis (math.FA); Metric Geometry (math.MG)

[42] arXiv:2207.01392 (cross-list from gr-qc) [pdf, other]

Title: Causal bubbles in globally hyperbolic spacetimes

Leonardo García-Heveling, Elefterios Soultanis

Comments: 5 pages, 1 figure

Journal-ref: Gen Relativ Gravit 54, 155 (2022)

Subjects: General Relativity and Quantum Cosmology (gr-qc); Mathematical Physics (math-ph); Differential Geometry (math.DG); Metric Geometry (math.MG)

[43] arXiv:2207.01985 (cross-list from math.CO) [pdf, other]

Title: Many regular triangulations and many polytopes

Arnau Padrol, Eva Philippe, Francisco Santos

Comments: 14 pages, 2 figures

Journal-ref: Math. Ann. 389 (2024), 745-763

Subjects: Combinatorics (math.CO); Metric Geometry (math.MG)

[44] arXiv:2207.02044 (cross-list from math.AP) [pdf, other]

Title: Isoperimetric sets and $p$-Cheeger sets are in bijection

Marco Caroccia, Giorgio Saracco

Journal-ref: J. Geom. Anal. 33:129, 2023

Subjects: Analysis of PDEs (math.AP); Metric Geometry (math.MG); Optimization and Control (math.OC)

[45] arXiv:2207.02259 (cross-list from math.CA) [pdf, html, other]

Title: A Furstenberg-type problem for circles, and a Kaufman-type restricted projection theorem in $\mathbb{R}^3$

Malabika Pramanik, Tongou Yang, Joshua Zahl

Comments: 37 pages, 3 figures. v3: final version, to appear in Amer. J. Math

Subjects: Classical Analysis and ODEs (math.CA); Metric Geometry (math.MG)

[46] arXiv:2207.02794 (cross-list from cs.DS) [pdf, other]

Title: Private Matrix Approximation and Geometry of Unitary Orbits

Oren Mangoubi, Yikai Wu, Satyen Kale, Abhradeep Guha Thakurta, Nisheeth K. Vishnoi

Journal-ref: Proceedings of Thirty Fifth Conference on Learning Theory (COLT), PMLR 178:3547-3588, 2022

Subjects: Data Structures and Algorithms (cs.DS); Cryptography and Security (cs.CR); Machine Learning (cs.LG); Metric Geometry (math.MG); Machine Learning (stat.ML)

[47] arXiv:2207.03077 (cross-list from math.CA) [pdf, other]

Title: On a topological Erd\H{o}s similarity problem

John Gallagher, Chun-Kit Lai, Eric Weber

Comments: Final Version. Referee comments incorporated

Subjects: Classical Analysis and ODEs (math.CA); Metric Geometry (math.MG)

[48] arXiv:2207.03310 (cross-list from math.CO) [pdf, other]

Title: Conic Frameworks Infinitesimal Rigidity

Colin Cros, Pierre-Olivier Amblard, Christophe Prieur, Jean-François Da Rocha

Subjects: Combinatorics (math.CO); Metric Geometry (math.MG)

[49] arXiv:2207.03715 (cross-list from math.DG) [pdf, html, other]

Title: Synthetic versus distributional lower Ricci curvature bounds

Michael Kunzinger, Michael Oberguggenberger, James A. Vickers

Comments: 23 pages, small correction in the proof of Th. 4.3

Journal-ref: Proceedings of the Royal Society of Edinburgh: Section A Mathematics 154 (2024) 1406-1430

Subjects: Differential Geometry (math.DG); Metric Geometry (math.MG)

[50] arXiv:2207.03897 (cross-list from math.AG) [pdf, other]

Title: Lipschitz trivial values of polynomial mappings

André Costa, Vincent Grandjean, Maria Michalska

Subjects: Algebraic Geometry (math.AG); Metric Geometry (math.MG)