Metric Geometry

Authors and titles for April 2025

[1] arXiv:2504.02139 (cross-list from math.MG) [cn-pdf, pdf, html, other]

Title: Uniquely realisable graphs in polyhedral normed spaces Show Chinese title

Title: 多面赋范空间中的唯一可实现图

Sean Dewar

Comments: 38 pages, 4 figures

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

[2] arXiv:2504.02276 (cross-list from math.MG) [cn-pdf, pdf, html, other]

Title: Distortion from spheres into Euclidean space Show Chinese title

Title: 从球面到欧几里得空间的畸变

James Dibble

Comments: 8 pages

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

[3] arXiv:2504.02656 (cross-list from math.MG) [cn-pdf, pdf, html, other]

Title: Covering spiky annuli by planks Show Chinese title

Title: 用木板覆盖尖刺环

Gergely Ambrus, Julian Huddell, Maggie Lai, Matthew Quirk, Elias Williams

Comments: 7 pages

Subjects: Metric Geometry (math.MG)

[4] arXiv:2504.02907 (cross-list from math.MG) [cn-pdf, pdf, html, other]

Title: Circular Isoptics in Flatland Show Chinese title

Title: 平面中的圆等角线

Alexander Thomas

Subjects: Metric Geometry (math.MG)

[5] arXiv:2504.03062 (cross-list from math.MG) [cn-pdf, pdf, other]

Title: Optimal transport on the sub-Lorentzian Heisenberg group Show Chinese title

Title: 关于次洛伦兹型海森堡群上的最优传输问题

Samuël Borza, Wilhelm Klingenberg, Patrick Wood

Comments: 34 pages

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

[6] arXiv:2504.03339 (cross-list from math.MG) [cn-pdf, pdf, html, other]

Title: On the (outer) Minkowski content with lower-dimensional structuring element Show Chinese title

Title: 关于具有低维结构元素的（外）Minkowski 内容

Markus Kiderlen, Jan Rataj

Comments: 23 pages

Subjects: Metric Geometry (math.MG)

[7] arXiv:2504.03362 (cross-list from math.MG) [cn-pdf, pdf, html, other]

Title: Metric spaces with small rough angles and the rectifiability of rough self-contracting curves Show Chinese title

Title: 度量空间中小粗糙角与粗糙自收缩曲线的可求长性

Estibalitz Durand-Cartagena, Jeremy T. Tyson

Comments: 45 pages. Version 2 includes minor edits and a new example (Appendix A) of a doubling metric space which is neither SRA free nor SRA full. We have also edited the acknowledgements and the bibliography

Subjects: Metric Geometry (math.MG)

[8] arXiv:2504.04286 (cross-list from math.MG) [cn-pdf, pdf, html, other]

Title: Comparison of Methods for Rotating a Point in $\mathbb{R}^3$: A Case Study Show Chinese title

Title: 比较旋转点的方法：$\mathbb{R}^3$案例研究

Tom Verhoeff

Comments: 13 pages, 5 figures

Subjects: Metric Geometry (math.MG)

[9] arXiv:2504.04594 (cross-list from math.MG) [cn-pdf, pdf, other]

Title: Distinct Distances Between a Line and Strip Show Chinese title

Title: 线与条带之间的不同距离

Sanjana Das, Adam Sheffer

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

[10] arXiv:2504.04720 (cross-list from math.MG) [cn-pdf, pdf, other]

Title: Fractal Zeta Functions and Complex Dimensions of Ahlfors Metric Measure Spaces Show Chinese title

Title: 分形zeta函数和Ahlfors度量测度空间的复数维数

Michel L. Lapidus, Sean Watson

Comments: 38 pages, 8 figures, submitted to Journal of Fractal Geometry

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

[11] arXiv:2504.04952 (cross-list from math.MG) [cn-pdf, pdf, html, other]

Title: The Vectorial Hadwiger Theorem on Convex Functions Show Chinese title

Title: 关于凸函数的向量值哈德瓦格定理

Mohamed A. Mouamine, Fabian Mussnig

Comments: New introduction; added references

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

[12] arXiv:2504.05042 (cross-list from math.MG) [cn-pdf, pdf, html, other]

Title: Lattice packing of spheres in high dimensions using a stochastically evolving ellipsoid Show Chinese title

Title: 高维球体的格子填充使用随机演化的椭球体

Boaz Klartag

Comments: 26 pages

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

[13] arXiv:2504.05412 (cross-list from math.MG) [cn-pdf, pdf, html, other]

Title: Stability of optimal transport maps on Riemannian manifolds Show Chinese title

Title: 黎曼流形上最优传输映射的稳定性

Jun Kitagawa, Cyril Letrouit, Quentin Mérigot

Comments: 22 pages, bibliography re-formatted, added example on sharpness of exponent, some typos fixed. Comments welcome!

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

[14] arXiv:2504.06186 (cross-list from math.MG) [cn-pdf, pdf, html, other]

Title: Equivalence between the timelike Brunn-Minkowski inequality and timelike Bakry-Émery-Ricci lower bound on weighted globally hyperbolic spacetimes Show Chinese title

Title: 加权整体双曲时空上类时Brunn-Minkowski不等式与类时Bakry-Émery-Ricci下界之间的等价性

Osama Farooqui

Subjects: Metric Geometry (math.MG) ; General Relativity and Quantum Cosmology (gr-qc)

[15] arXiv:2504.06456 (cross-list from math.MG) [cn-pdf, pdf, html, other]

Title: Characterization of higher rank via affine maps Show Chinese title

Title: 通过仿射映射的高阶特征化

David Lenze

Comments: 16 pages, 4 figures. Published in Geom. Dedicata 219, 79 (2025); revised based on the referee's comments

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

[16] arXiv:2504.06743 (cross-list from math.MG) [cn-pdf, pdf, html, other]

Title: Kinematic formulas in convex geometry for non-compact groups Show Chinese title

Title: 非紧致群在凸几何中的运动公式

Sílvia Anjos, Francisco Nascimento

Comments: 13 pages. Comments welcome

Subjects: Metric Geometry (math.MG)

[17] arXiv:2504.07700 (cross-list from math.MG) [cn-pdf, pdf, html, other]

Title: The geometry of inconvenience and perverse equilibria in trade networks Show Chinese title

Title: 贸易网络中的不便几何与扭曲均衡

Michael Coopman, Austin Jacobs, Henry Pascoe, J. E. Pascoe

Comments: 25 Pages

Subjects: Metric Geometry (math.MG) ; Theoretical Economics (econ.TH) ; Functional Analysis (math.FA)

[18] arXiv:2504.08127 (cross-list from math.MG) [cn-pdf, pdf, other]

Title: Quasisymmetric rectifiability of uniformly disconnected sets Show Chinese title

Title: 拟对称可求积的均匀不连通集

Jacob Honeycutt, Vyron Vellis

Comments: 34 pages, 5 figures

Subjects: Metric Geometry (math.MG)

[19] arXiv:2504.09251 (cross-list from math.MG) [cn-pdf, pdf, html, other]

Title: Affine Logarithmic HLS and Beckner-Type Logarithmic Sobolev Inequalities Show Chinese title

Title: 仿射对数HLS和Beckner型对数Sobolev不等式

Xiaxing Cai

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

[20] arXiv:2504.12117 (cross-list from math.MG) [cn-pdf, pdf, html, other]

Title: The $L_p$ Minkowski problems on affine dual quermassintegrals Show Chinese title

Title: 关于仿射 dual 混合体积的$L_p$闵可夫斯基问题

Youjiang Lin, Yuchi Wu

Comments: arXiv admin note: text overlap with arXiv:1802.00933 by other authors

Subjects: Metric Geometry (math.MG)

[21] arXiv:2504.12866 (cross-list from math.MG) [cn-pdf, pdf, other]

Title: Intersections of random chords of a circle Show Chinese title

Title: 圆的随机弦的交点

Cynthia Bortolotto, Victor Souza

Comments: Unrefereed draft, final version to appear in The American Mathematical Monthly

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

[22] arXiv:2504.13013 (cross-list from math.MG) [cn-pdf, pdf, other]

Title: Minkowski chirality: a measure of reflectional asymmetry of convex bodies Show Chinese title

Title: 闵可夫斯基手性：凸体反射不对称性的度量

Andrei Caragea, Katherina von Dichter, Kurt Klement Gottwald, Florian Grundbacher, Thomas Jahn, Mia Runge

Subjects: Metric Geometry (math.MG)

[23] arXiv:2504.13571 (cross-list from math.MG) [cn-pdf, pdf, html, other]

Title: On the Figiel-Lindenstrauss-Milman inequality Show Chinese title

Title: 关于Figiel-Lindenstrauss-Milman不等式

Tomer Milo

Subjects: Metric Geometry (math.MG)

[24] arXiv:2504.14567 (cross-list from math.MG) [cn-pdf, pdf, html, other]

Title: Hopf-type theorems for convex surfaces Show Chinese title

Title: 霍普型定理对于凸曲面

I.M.Shirokov

Comments: 9 pages, 2 figures

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

[25] arXiv:2504.14629 (cross-list from math.MG) [cn-pdf, pdf, html, other]

Title: New geodesic lines in the Gromov-Hausdorff class lying in the cloud of the real line Show Chinese title

Title: Gromov-Hausdorff类中位于实线云中的新测地线

Ivan N. Mikhailov

Comments: 9 pages, 2 pictures, accepted for publication in Chebyshevskii Sbornik

Subjects: Metric Geometry (math.MG)

[26] arXiv:2504.15060 (cross-list from math.MG) [cn-pdf, pdf, html, other]

Title: Flexible polyhedral nets in isotropic geometry Show Chinese title

Title: 各向同性几何中的灵活多面体网

O. Pirahmad, H. Pottmann, M. Skopenkov

Comments: 35 pages, 12 figures

Subjects: Metric Geometry (math.MG)

[27] arXiv:2504.15488 (cross-list from math.MG) [cn-pdf, pdf, html, other]

Title: Floating bodies for ball-convex bodies Show Chinese title

Title: 关于球凸体的浮体

Carsten Schuett, Elisabeth M Werner, Diliya Yalikun

Subjects: Metric Geometry (math.MG)

[28] arXiv:2504.17530 (cross-list from math.MG) [cn-pdf, pdf, html, other]

Title: Hollow polytopes with many vertices Show Chinese title

Title: 空心多胞体具有多个顶点

Srinivas Arun, Travis Dillon

Comments: 7 pages. This article replaces Section 3 in arXiv:2409.07262v1 after splitting that article into two papers

Subjects: Metric Geometry (math.MG)

[29] arXiv:2504.19753 (cross-list from math.MG) [cn-pdf, pdf, other]

Title: A New Decision- Making Method Based on Shannon Entropy Analysis Show Chinese title

Title: 基于香农熵分析的新决策方法

Hamid Babaei, Shabnam Mohammadi, Hossein Ghaneai

Comments: Advances in Operations research

Subjects: Metric Geometry (math.MG)

[30] arXiv:2504.20779 (cross-list from math.MG) [cn-pdf, pdf, html, other]

Title: Examples of aspherical Alexandrov spaces Show Chinese title

Title: 非球面Alexandrov空间的例子

Michael Kapovich

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

[31] arXiv:2504.00932 (cross-list from math.CO) [cn-pdf, pdf, other]

Title: Strongly sublinear separators and bounded asymptotic dimension for sphere intersection graphs Show Chinese title

Title: 强子线性分隔符和有界渐近维度的球面交集图

James Davies, Agelos Georgakopoulos, Meike Hatzel, Rose McCarty

Comments: 20 pages, 2 figures

Subjects: Combinatorics (math.CO) ; Computational Geometry (cs.CG) ; Discrete Mathematics (cs.DM) ; Metric Geometry (math.MG)

[32] arXiv:2504.01864 (cross-list from math.FA) [cn-pdf, pdf, html, other]

Title: On the $W$-entropy and Shannon entropy power on RCD$(K, N)$ and RCD$(K, n, N)$ spaces Show Chinese title

Title: 关于 RCD$W$熵和 Shannon 熵功率的 RCD$(K, N)$和 RCD$(K, n, N)$空间

Xiang-Dong Li, Enrui Zhang

Comments: Add Section 9

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

[33] arXiv:2504.02700 (cross-list from math.NA) [cn-pdf, pdf, html, other]

Title: Centroidal Voronoi Tessellations as Electrostatic Equilibria: A Generalized Thomson Problem in Convex Domains Show Chinese title

Title: 重心Voronoi镶嵌作为静电平衡：凸域中的广义汤姆森问题

Zachary Mullaghy

Subjects: Numerical Analysis (math.NA) ; Mathematical Physics (math-ph) ; Metric Geometry (math.MG) ; Optimization and Control (math.OC)

[34] arXiv:2504.02741 (cross-list from math.CA) [cn-pdf, pdf, html, other]

Title: A Complete Classification of Fourier Summation Formulas on the real line Show Chinese title

Title: 实线上傅里叶求和公式的完全分类

Felipe Gonçalves, Guilherme Vedana

Comments: 19 pages

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

[35] arXiv:2504.03114 (cross-list from math.PR) [cn-pdf, pdf, html, other]

Title: Entropy and functional forms of the dimensional Brunn--Minkowski inequality in Gauss space Show Chinese title

Title: 高斯空间中维度的Brunn-Minkowski不等式的熵和函数形式

Gautam Aishwarya, Dongbin Li

Comments: 17 pages, comments welcome!

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

[36] arXiv:2504.03356 (cross-list from math.DG) [cn-pdf, pdf, html, other]

Title: Gluing $CAT(0)$ domains Show Chinese title

Title: 粘贴$CAT(0)$域

Charalampos Charitos, Ioannis Papadoperakis, Georgios Tsapogas

Comments: 32 pages, 9 figures

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

[37] arXiv:2504.04337 (cross-list from math.FA) [cn-pdf, pdf, html, other]

Title: The Gaussian correlation inequality for centered convex sets and the case of equality Show Chinese title

Title: 中心凸集的高斯相关性不等式及等号成立的情况

Shohei Nakamura, Hiroshi Tsuji

Comments: 34 pages. Changed the title, fixed the condition (3.4), and added Section 5 in which the case of equality is discussed

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

[38] arXiv:2504.05194 (cross-list from math.DS) [cn-pdf, pdf, html, other]

Title: A general framework for quasi-isometries in symbolic dynamics beyond groups Show Chinese title

Title: 准等距映射在符号动力学中的一般框架：超越群的视角

Sebastián Barbieri, Nicolás Bitar

Comments: 34 pages, 7 figures. Comments welcome!

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

[39] arXiv:2504.05459 (cross-list from math.DG) [cn-pdf, pdf, other]

Title: Length of a closed geodesic in 3-manifolds of positive scalar curvature Show Chinese title

Title: 正数量曲率3流形中闭测地线的长度

Yevgeny Liokumovich, Davi Maximo, Regina Rotman

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

[40] arXiv:2504.05719 (cross-list from math.HO) [cn-pdf, pdf, other]

Title: Mental Geometry Show Chinese title

Title: 心智几何学

Nicolas Bouleau (ENPC)

Journal-ref: Le Bulletin Vert = Bulletin de l'APMEP, 1999, 423, pp.163-171

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

[41] arXiv:2504.06865 (cross-list from math.DG) [cn-pdf, pdf, html, other]

Title: On manifolds with almost non-negative Ricci curvature and integrally-positive $k^{th}$-scalar curvature Show Chinese title

Title: 关于具有几乎非负Ricci曲率和积分正的$k^{th}$-数量曲率的流形

Alessandro Cucinotta, Andrea Mondino

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

[42] arXiv:2504.09241 (cross-list from math.CO) [cn-pdf, pdf, other]

Title: Real-rooted integer polynomial enumeration algorithms and interlacing polynomials via linear programming Show Chinese title

Title: 具有实根的整系数多项式枚举算法与通过线性规划的交错多项式

Gary R.W. Greaves, Jeven Syatriadi

Comments: 25 pages

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

[43] arXiv:2504.09320 (cross-list from math.DG) [cn-pdf, pdf, html, other]

Title: Capillary Christoffel-Minkowski problem Show Chinese title

Title: 毛细Christoffel-Minkowski问题

Yingxiang Hu, Mohammad N. Ivaki, Julian Scheuer

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

[44] arXiv:2504.09503 (cross-list from math.FA) [cn-pdf, pdf, html, other]

Title: $p$-Poincaré inequalities and cutoff Sobolev inequalities on metric measure spaces Show Chinese title

Title: $p$-度量测度空间上的Poincaré不等式和截断Sobolev不等式

Meng Yang

Comments: 49 pages, major revision. The capacity upper bound is replaced by the cutoff Sobolev inequality, which is much stronger. The proof of this new condition is added in Proposition 4.4 and Proposition 6.5. A new section (Section 8) on potential theory is added to clarify the definition of this new condition and to provide the necessary tools for its proof

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

[45] arXiv:2504.10380 (cross-list from math.DG) [cn-pdf, pdf, html, other]

Title: Lorentzian Gromov-Hausdorff convergence and pre-compactness Show Chinese title

Title: 洛伦兹Gromov-Hausdorff收敛和预紧性

Andrea Mondino, Clemens Sämann

Comments: 67 pages; v3: new subsection 8.2 on curvature-driven pre-compactness and minor corrections

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

[46] arXiv:2504.10758 (cross-list from math.DG) [cn-pdf, pdf, other]

Title: Allard's interior $\varepsilon$-Regularity Theorem in Alexandrov spaces Show Chinese title

Title: 亚历山德罗夫空间中的Allard内蕴$\varepsilon$-正则性定理

Marcos Agnoletto, Julio C. Correa Hoyos, Márcio Fabiano da Silva, Stefano Nardulli

Comments: 88 pages, 5 figures, any comments or suggestions are welcome. Please send them to Marcos Agnoletto at marcos.forte@ufabc.edu.br. In the second version, we corrected a typo that appeared in Theorem A, Theorem B, and Corollary A. Specifically, we replaced $p \in \mathbb{N}$ with $p \in \mathbb{R}$ and added new references

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

[47] arXiv:2504.11086 (cross-list from math.CO) [cn-pdf, pdf, html, other]

Title: Obtuse almost-equiangular sets Show Chinese title

Title: 钝角几乎等角集

Christine Bachoc, Bram Bekker, Philippe Moustrou, Fernando Mário de Oliveira Filho

Comments: 29 pages; fixed problem with references from previous version

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

[48] arXiv:2504.11302 (cross-list from math.CA) [cn-pdf, pdf, html, other]

Title: Limits of Discrete Energy of Families of Increasing Sets Show Chinese title

Title: 增加集族的离散能量极限

Hari Sarang Nathan

Subjects: Classical Analysis and ODEs (math.CA) ; Machine Learning (cs.LG) ; Metric Geometry (math.MG)

[49] arXiv:2504.11619 (cross-list from math.AG) [cn-pdf, pdf, html, other]

Title: Computing the Tropical Abel--Jacobi Transform and Tropical Distances for Metric Graphs Show Chinese title

Title: 计算度量图的热带阿贝尔-雅可比变换和热带距离

Yueqi Cao, Anthea Monod

Comments: 51 pages, 9 figures

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

[50] arXiv:2504.14161 (cross-list from math.ST) [cn-pdf, pdf, html, other]

Title: Robust Estimation in metric spaces: Achieving Exponential Concentration with a Fréchet Median Show Chinese title

Title: 度量空间中的鲁棒估计：通过弗雷歇中位数实现指数集中性

Jakwang Kim, Jiyoung Park, Anirban Bhattacharya

Journal-ref: Proceedings of the 28th International Conference on Artificial Intelligence and Statistics (AISTATS) 2025, PMLR 258

Subjects: Statistics Theory (math.ST) ; Metric Geometry (math.MG) ; Machine Learning (stat.ML)