Differential Geometry

Authors and titles for January 2024

[151] arXiv:2401.00780 (cross-list from gr-qc) [cn-pdf, pdf, html, other]

Title: Symmetries in Riemann-Cartan Geometries Show Chinese title

Title: 黎曼-卡特安几何中的对称性

David D. McNutt, Alan A. Coley, Robert J. van den Hoogen

Journal-ref: SIGMA 20 (2024), 078, 20 pages

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

[152] arXiv:2401.00791 (cross-list from math.AP) [cn-pdf, pdf, html, other]

Title: Normal operators for momentum ray transforms, I: The inversion formula Show Chinese title

Title: 动量射线变换的正规算子，I：反演公式

Shubham R. Jathar, Manas Kar, Venkateswaran P. Krishnan, Vladimir A. Sharafutdinov

Comments: 29 pages. This manuscript has been accepted for publication in the Journal of Fourier Analysis and Applications

Journal-ref: The Journal of Fourier Analysis and Applications 30, 58 (2024)

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

[153] arXiv:2401.01034 (cross-list from math.AP) [cn-pdf, pdf, html, other]

Title: Hessian estimates for special Lagrangian equation by doubling Show Chinese title

Title: 利用加倍方法的特殊拉格朗日方程的Hessian估计

Ravi Shankar

Comments: 15 pg

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

[154] arXiv:2401.01129 (cross-list from math.OC) [cn-pdf, pdf, html, other]

Title: Reduction by Symmetry and Optimal Control with Broken Symmetries on Riemannian Manifolds Show Chinese title

Title: 对称性约简与在黎曼流形上的破缺对称性的最优控制

Jacob R. Goodman, Leonardo J. Colombo

Comments: 33 pages. arXiv admin note: text overlap with arXiv:2207.13574

Subjects: Optimization and Control (math.OC) ; Systems and Control (eess.SY) ; Differential Geometry (math.DG) ; Dynamical Systems (math.DS)

[155] arXiv:2401.01700 (cross-list from math-ph) [cn-pdf, pdf, html, other]

Title: Tulczyjew triple on the Atiyah algebroid with connection Show Chinese title

Title: 带有联络的Atiyah代数结构的Tulczyjew三元组

Katarzyna Grabowska, Paweł Korzeb, Kuba Krawczyk

Subjects: Mathematical Physics (math-ph) ; Differential Geometry (math.DG)

[156] arXiv:2401.02003 (cross-list from gr-qc) [cn-pdf, pdf, other]

Title: Naked Singularity Censoring with Anisotropic Apparent Horizon Show Chinese title

Title: 裸奇点 censorship 的各向异性视界

Xinliang An

Comments: 90 pages, announced in December 2022

Journal-ref: Ann. of Math, 201(3), (2025), 775-908

Subjects: General Relativity and Quantum Cosmology (gr-qc) ; Mathematical Physics (math-ph) ; Analysis of PDEs (math.AP) ; Differential Geometry (math.DG)

[157] arXiv:2401.02010 (cross-list from math.AG) [cn-pdf, pdf, html, other]

Title: Numerical semistability of projective toric varieties Show Chinese title

Title: 射影环面簇的数值半稳定性

Naoto Yotsutani

Comments: The title has been slightly changed. We adapt the following terminology for semistability of a pair. Semistability is defined to be disjoint orbit closures. Numerical semistability is defined as the inclusion of weight polytopes

Subjects: Algebraic Geometry (math.AG) ; Differential Geometry (math.DG)

[158] arXiv:2401.02242 (cross-list from math.AP) [cn-pdf, pdf, other]

Title: Energy Identity for Stationary Harmonic Maps Show Chinese title

Title: 能量恒等式对于静止的调和映射

Aaron Naber, Daniele Valtorta

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

[159] arXiv:2401.02560 (cross-list from math.GT) [cn-pdf, pdf, html, other]

Title: Asymptotic dimension and geometric decompositions in dimensions 3 and 4 Show Chinese title

Title: 渐近维数和三维与四维中的几何分解

H. Contreras Peruyero, P. Suárez-Serrato

Comments: 22 pages, 2 images

Subjects: Geometric Topology (math.GT) ; Differential Geometry (math.DG) ; Group Theory (math.GR)

[160] arXiv:2401.02577 (cross-list from math.SG) [cn-pdf, pdf, html, other]

Title: Non-archimedean analytic continuation of unobstructedness Show Chinese title

Title: 非阿基米德解析延拓的无阻碍性

Hang Yuan

Comments: Final version. Accepted by Quantum Topology

Subjects: Symplectic Geometry (math.SG) ; Algebraic Geometry (math.AG) ; Differential Geometry (math.DG)

[161] arXiv:2401.02667 (cross-list from math.SG) [cn-pdf, pdf, html, other]

Title: Global Hypersurfaces of Section for Geodesic Flows on Convex Hypersurfaces Show Chinese title

Title: 测地流在凸超曲面上的全局横截超曲面

Sunghae Cho, Dongho Lee

Comments: 11 pages

Journal-ref: Archive der Mathematik (Basel) 123, 291-307 (2024)

Subjects: Symplectic Geometry (math.SG) ; Differential Geometry (math.DG)

[162] arXiv:2401.02762 (cross-list from math.MG) [cn-pdf, pdf, html, other]

Title: Poincaré inequality and energy of separating sets Show Chinese title

Title: Poincaré不等式和分离集的能量

Emanuele Caputo, Nicola Cavallucci

Comments: 37 pages, 1 figure. Comments are welcome

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

[163] arXiv:2401.03460 (cross-list from math.GT) [cn-pdf, pdf, html, other]

Title: Five tori in $S^4$ Show Chinese title

Title: 五个环面在$S^4$

Bruno Martelli

Comments: 35 pages, 24 figures

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

[164] arXiv:2401.03949 (cross-list from math.MG) [cn-pdf, pdf, html, other]

Title: A sharp isoperimetric-type inequality for Lorentzian spaces satisfying timelike Ricci lower bounds Show Chinese title

Title: 满足类时 Ricci 低界的 Lorentzian 空间的一个精确的等周不等式

Fabio Cavalletti, Andrea Mondino

Comments: Improved both the results and the presentation. 53 pages

Subjects: Metric Geometry (math.MG) ; Mathematical Physics (math-ph) ; Differential Geometry (math.DG)

[165] arXiv:2401.04048 (cross-list from gr-qc) [cn-pdf, pdf, html, other]

Title: Gluing-at-infinity of two-dimensional asymptotically locally hyperbolic manifolds Show Chinese title

Title: 二维渐近局部双曲流形在无穷处的粘合

Piotr T. Chruściel, Raphaela Wutte

Comments: 53 pages, 9 figures, v2: expanded to include the analysis of global properties of some solutions

Subjects: General Relativity and Quantum Cosmology (gr-qc) ; High Energy Physics - Theory (hep-th) ; Differential Geometry (math.DG)

[166] arXiv:2401.04071 (cross-list from cs.CV) [cn-pdf, pdf, html, other]

Title: Fun with Flags: Robust Principal Directions via Flag Manifolds Show Chinese title

Title: 与旗帜相关的趣味：通过旗帜流形的鲁棒主方向

Nathan Mankovich, Gustau Camps-Valls, Tolga Birdal

Subjects: Computer Vision and Pattern Recognition (cs.CV) ; Machine Learning (cs.LG) ; Differential Geometry (math.DG) ; Optimization and Control (math.OC) ; Machine Learning (stat.ML)

[167] arXiv:2401.04409 (cross-list from math.AP) [cn-pdf, pdf, html, other]

Title: Semi-classical Heat Kernel Asymptotics and Morse Inequalities Show Chinese title

Title: 半经典热核渐近和莫尔斯不等式

Eric Jian-Ting Chen

Comments: 38 pages. This is the adapted version of the author's master thesis

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

[168] arXiv:2401.04442 (cross-list from gr-qc) [cn-pdf, pdf, other]

Title: Characteristic Gluing with $Λ$: II. Linearised equations in higher dimensions Show Chinese title

Title: 特征粘接与$Λ$：II。 高维中的线性化方程

Wan Cong, Piotr T. Chruściel, Finnian Gray

Comments: v2; update includes changes and additions to streamline compatibility with part III---the nonlinear gluing. 145 pages, 72 main text plus appendices and index, 4 figures, results summarised in 4 tables

Subjects: General Relativity and Quantum Cosmology (gr-qc) ; Mathematical Physics (math-ph) ; Analysis of PDEs (math.AP) ; Differential Geometry (math.DG)

[169] arXiv:2401.04822 (cross-list from math.AP) [cn-pdf, pdf, html, other]

Title: On minimizers in the liquid drop model Show Chinese title

Title: 关于液体滴模型中的极小值问题

Otis Chodosh, Ian Ruohoniemi

Comments: Comments welcome! Minor edits. Final version, to appear in CPAM

Subjects: Analysis of PDEs (math.AP) ; Mathematical Physics (math-ph) ; Differential Geometry (math.DG)

[170] arXiv:2401.05179 (cross-list from math.FA) [cn-pdf, pdf, html, other]

Title: Intertwining Curvature Bounds for Graphs and Quantum Markov Semigroups Show Chinese title

Title: 图和量子马尔可夫半群的交织曲率边界

Florentin Münch, Melchior Wirth, Haonan Zhang

Subjects: Functional Analysis (math.FA) ; Differential Geometry (math.DG) ; Quantum Physics (quant-ph)

[171] arXiv:2401.05253 (cross-list from gr-qc) [cn-pdf, pdf, html, other]

Title: Black Hole and Equipotential Photon Surface Uniqueness in 4-dimensional Asymptotically Flat Electrostatic Electro-Vacuum Spacetimes Show Chinese title

Title: 黑洞和等势光子表面在四维渐近平坦静电电真空时空中的唯一性

Stefano Borghini, Carla Cederbaum, Albachiara Cogo

Comments: 63 pages

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

[172] arXiv:2401.05274 (cross-list from math.SG) [cn-pdf, pdf, html, other]

Title: On Complex Lie Algebroids with Constant Real Rank Show Chinese title

Title: 关于具有常实秩的复李代数胚

Dan Aguero

Journal-ref: SIGMA 21 (2025), 044, 25 pages

Subjects: Symplectic Geometry (math.SG) ; Differential Geometry (math.DG)

[173] arXiv:2401.05275 (cross-list from hep-th) [cn-pdf, pdf, other]

Title: Higher Gauge Theory Show Chinese title

Title: 高阶规范理论

Leron Borsten, Mehran Jalali Farahani, Branislav Jurco, Hyungrok Kim, Jiri Narozny, Dominik Rist, Christian Saemann, Martin Wolf

Comments: v2: typos fixed, presentation improved, published version

Journal-ref: Encyclopedia of Mathematical Physics (Second Edition), 4 (2025) 159-185

Subjects: High Energy Physics - Theory (hep-th) ; Mathematical Physics (math-ph) ; Differential Geometry (math.DG)

[174] arXiv:2401.06572 (cross-list from math.SG) [cn-pdf, pdf, html, other]

Title: A rigidity result for coisotropic submanifolds in contact geometry Show Chinese title

Title: 接触几何中余法子流形的一个刚性结果

Stephane Geudens, Alfonso G. Tortorella

Comments: Minor stylistic modifications. Final version to appear in Math. Z

Subjects: Symplectic Geometry (math.SG) ; Differential Geometry (math.DG)

[175] arXiv:2401.06607 (cross-list from math.GT) [cn-pdf, pdf, html, other]

Title: Envelopes of the Thurston metric on Teichmüller space Show Chinese title

Title: 泰希穆勒空间上汤普森度量的包络线

Huiping Pan, Michael Wolf

Comments: 65 pages, no figures. All comments are welcome

Subjects: Geometric Topology (math.GT) ; Complex Variables (math.CV) ; Differential Geometry (math.DG)

[176] arXiv:2401.06694 (cross-list from math.AG) [cn-pdf, pdf, other]

Title: Topological recursion and variations of spectral curves for twisted Higgs bundles Show Chinese title

Title: 拓扑递归与扭曲Higgs丛的谱曲线变化

Christopher Mahadeo, Steven Rayan

Comments: 53 pages, 5 figures

Subjects: Algebraic Geometry (math.AG) ; Mathematical Physics (math-ph) ; Complex Variables (math.CV) ; Differential Geometry (math.DG) ; Symplectic Geometry (math.SG)

[177] arXiv:2401.06702 (cross-list from gr-qc) [cn-pdf, pdf, html, other]

Title: On the existence of charged electrostatic black holes in arbitrary topology Show Chinese title

Title: 关于任意拓扑下带电静电黑洞的存在性

Martin Reiris

Comments: 20 pages, 1 figure

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

[178] arXiv:2401.06736 (cross-list from math.AP) [cn-pdf, pdf, html, other]

Title: A fundamental solution for a subelliptic operator in Finsler geometry Show Chinese title

Title: 一个子椭圆算子的基本解在芬斯勒几何中

Federica Dragoni, Nicola Garofalo, Gianmarco Giovannardi, Paolo Salani

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

[179] arXiv:2401.06956 (cross-list from math.CV) [cn-pdf, pdf, html, other]

Title: A note on Rational Maps with three branching points on the Riemann sphere Show Chinese title

Title: 关于黎曼球面上具有三个分支点的有理映射的一篇笔记

Zhiqiang Wei, Yingyi Wu, Bin Xu

Comments: 9 pages. We have revised certain sentences, corrected several errors, and added additional content to enhance the clarity and depth of our paper. Comments are welcome

Subjects: Complex Variables (math.CV) ; Differential Geometry (math.DG)

[180] arXiv:2401.07195 (cross-list from math.CV) [cn-pdf, pdf, html, other]

Title: On the Gauss maps of complete minimal surfaces in $\mathbb{R}^n$ Show Chinese title

Title: 关于完备极小曲面的高斯映射在$\mathbb{R}^n$中

Dinh Tuan Huynh

Comments: 13 pages, comments are welcome. arXiv admin note: text overlap with arXiv:2012.12656, arXiv:1704.03358

Journal-ref: Pacific J. Math. 330 (2024) 157-170

Subjects: Complex Variables (math.CV) ; Differential Geometry (math.DG)

[181] arXiv:2401.07225 (cross-list from gr-qc) [cn-pdf, pdf, html, other]

Title: What Uniqueness for the Holst-Nagy-Tsogtgerel--Maxwell Solutions to the Einstein Conformal Constraint Equations? Show Chinese title

Title: Holst-Nagy-Tsogtgerel--Maxwell 解在爱因斯坦共形约束方程中的唯一性是什么？

Romain Gicquaud

Comments: 21 pages, comments welcome!

Subjects: General Relativity and Quantum Cosmology (gr-qc) ; Analysis of PDEs (math.AP) ; Differential Geometry (math.DG)

[182] arXiv:2401.07474 (cross-list from math.OA) [cn-pdf, pdf, html, other]

Title: Equivariant Index Theorem on $\mathbb{R}^n$ in the Context of Continuous Fields of $C^*$-algebras Show Chinese title

Title: 连续域上的 $\mathbb{R}^n$ 的等变指标定理在 $C^*$-代数的背景下

Baiying Ren, Hang Wang, Zijing Wang

Subjects: Operator Algebras (math.OA) ; Differential Geometry (math.DG)

[183] arXiv:2401.07555 (cross-list from math.OC) [cn-pdf, pdf, html, other]

Title: Distributions and controllability problems (I) Show Chinese title

Title: 分布和可控性问题（一）

Cristina Giannotti, Andrea Spiro, Marta Zoppello

Comments: 50 pages, 3 figures This paper is a revision of the previous manuscript, now we removed an unnecessary assumption, enhancing in this way all results, which now hold in a much more general setting

Subjects: Optimization and Control (math.OC) ; Differential Geometry (math.DG)

[184] arXiv:2401.07667 (cross-list from math.FA) [cn-pdf, pdf, other]

Title: Adiabatic Limit of Calderon Projector on Manifold with Cylindrical End Show Chinese title

Title: 渐近绝热极限下的柱面端流形上的Calderon投影算子

Kunal Sharma

Comments: Comments are welcome

Subjects: Functional Analysis (math.FA) ; Differential Geometry (math.DG)

[185] arXiv:2401.07735 (cross-list from math.AG) [cn-pdf, pdf, other]

Title: Plücker Coordinates and the Rosenfeld Planes Show Chinese title

Title: 普吕克坐标和罗森菲尔德平面

Jian Qiu

Comments: 44 pages, final version published in J.Geom.Phys

Journal-ref: J.Geom.Phys. 206 (2024) 105331

Subjects: Algebraic Geometry (math.AG) ; High Energy Physics - Theory (hep-th) ; Differential Geometry (math.DG) ; Symplectic Geometry (math.SG)

[186] arXiv:2401.07808 (cross-list from math.AP) [cn-pdf, pdf, other]

Title: Fully nonlinear Yamabe-type problems on non-compact manifolds Show Chinese title

Title: 完全非线性Yamabe型问题在非紧流形上

Jonah A. J. Duncan, Yi Wang

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

[187] arXiv:2401.07920 (cross-list from math.SG) [cn-pdf, pdf, other]

Title: Implosion, Contraction and Moore-Tachikawa Show Chinese title

Title: 爆缩，收缩和莫尔-塔奇卡瓦

Andrew Dancer, Frances Kirwan, Johan Martens

Comments: 23 Pages. To appear in Int. J. Math. (special issue in honour of Oscar Garcia Prada)

Journal-ref: Internat. J. Math.35(2024), no.9, Paper No. 2441004

Subjects: Symplectic Geometry (math.SG) ; Algebraic Geometry (math.AG) ; Differential Geometry (math.DG)

[188] arXiv:2401.08063 (cross-list from math.AP) [cn-pdf, pdf, html, other]

Title: An Infinite Double Bubble Theorem Show Chinese title

Title: 无穷双气泡定理

Lia Bronsard, Michael Novack

Comments: to appear in Ann. Inst. H. Poincar\'e C Anal. Non Lin\'eaire

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

[189] arXiv:2401.08198 (cross-list from gr-qc) [cn-pdf, pdf, other]

Title: A model for cosmological perturbations in affine gravity Show Chinese title

Title: 仿射引力中宇宙扰动的模型

Oscar Castillo-Felisola, Radouane Gannouji, Manuel Morocho-López, Marcelo Rozas-Rojas

Comments: Written using revtex, 12 pages

Subjects: General Relativity and Quantum Cosmology (gr-qc) ; High Energy Physics - Theory (hep-th) ; Mathematical Physics (math-ph) ; Differential Geometry (math.DG)

[190] arXiv:2401.08243 (cross-list from math.CV) [cn-pdf, pdf, html, other]

Title: Random Systems of Holomorphic Sections of a Sequence of Line bundles on Compact Kähler Manifolds Show Chinese title

Title: 紧Kähler流形上一族线丛的全纯截面的随机系统

Afrim Bojnik, Ozan Günyüz

Comments: 24 pages, some revisions

Subjects: Complex Variables (math.CV) ; Differential Geometry (math.DG) ; Probability (math.PR)

[191] arXiv:2401.08403 (cross-list from math.AP) [cn-pdf, pdf, html, other]

Title: The Quantization of Maxwell Theory in the Cauchy Radiation Gauge: Hodge Decomposition and Hadamard States Show Chinese title

Title: 麦克斯韦理论在柯西辐射规范中的量化：霍奇分解与哈达玛态

Simone Murro, Gabriel Schmid

Comments: 38 pages -- to appear in J. Lond. Math. Soc

Journal-ref: J. London Math. Soc. 110(5):e70020, 2024

Subjects: Analysis of PDEs (math.AP) ; Mathematical Physics (math-ph) ; Differential Geometry (math.DG) ; Functional Analysis (math.FA)

[192] arXiv:2401.08540 (cross-list from math-ph) [cn-pdf, pdf, other]

Title: Asymptotic Equivalence of Identification Operators in Geometric Scattering Theory Show Chinese title

Title: 几何散射理论中识别算子的渐近等价性

Batu Güneysu

Subjects: Mathematical Physics (math-ph) ; Differential Geometry (math.DG) ; Spectral Theory (math.SP)

[193] arXiv:2401.08842 (cross-list from math.SG) [cn-pdf, pdf, other]

Title: The chord conjecture for conormal bundles Show Chinese title

Title: 绳索猜想对于法丛

Filip Broćić, Dylan Cant, Egor Shelukhin

Comments: 58 pages, 22 figures

Subjects: Symplectic Geometry (math.SG) ; Differential Geometry (math.DG)

[194] arXiv:2401.09143 (cross-list from math.CV) [cn-pdf, pdf, other]

Title: Induced Fubini-Study metrics on strictly pseudoconvex CR manifolds and zeros of random CR functions Show Chinese title

Title: 严格伪凸CR流形上的诱导Fubini-Study度量和随机CR函数的零点

Hendrik Herrmann, Chin-Yu Hsiao, George Marinescu, Wei-Chuan Shen

Comments: 63 pages

Subjects: Complex Variables (math.CV) ; Analysis of PDEs (math.AP) ; Differential Geometry (math.DG) ; Probability (math.PR)

[195] arXiv:2401.09293 (cross-list from math.CA) [cn-pdf, pdf, html, other]

Title: Restricted Mean Value Property with non-tangential boundary behavior on Riemannian manifolds Show Chinese title

Title: 非切向边界行为下的黎曼流形上的限制平均值性质

Utsav Dewan

Comments: arXiv admin note: text overlap with arXiv:2307.05215

Subjects: Classical Analysis and ODEs (math.CA) ; Differential Geometry (math.DG)

[196] arXiv:2401.09319 (cross-list from math.AP) [cn-pdf, pdf, html, other]

Title: Positive solutions of a critical equation in sub-Finsler geometry Show Chinese title

Title: 临界方程在次Finsler几何中的正解

Nicola Garofalo, Paolo Salani

Comments: arXiv admin note: text overlap with arXiv:2401.06736

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

[197] arXiv:2401.09337 (cross-list from math-ph) [cn-pdf, pdf, html, other]

Title: Gravity Coupled with Scalar, SU$(n)$, and Spinor Fields on Manifolds with Null-Boundary Show Chinese title

Title: 引力与标量、SU$(n)$和旋量场在具零边界的流形上

Alberto S. Cattaneo, Filippo Fila-Robattino, Valentino Huang, Manuel Tecchiolli

Subjects: Mathematical Physics (math-ph) ; High Energy Physics - Theory (hep-th) ; Differential Geometry (math.DG) ; Symplectic Geometry (math.SG)

[198] arXiv:2401.09612 (cross-list from math.AP) [cn-pdf, pdf, html, other]

Title: A note on sign-changing solutions to supercritical Yamabe-type equations Show Chinese title

Title: 关于超临界Yamabe型方程的变号解的一篇注记

Jurgen Julio-Batalla

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

[199] arXiv:2401.09982 (cross-list from math.MG) [cn-pdf, pdf, html, other]

Title: Second-order estimates for the $p$-Laplacian in RCD spaces Show Chinese title

Title: 二阶估计在RCD空间中的$p$-拉普拉斯算子

Luca Benatti, Ivan Yuri Violo

Comments: Minor corrections, published version in JDE (doi:10.1016/j.jde.2025.113398). Comments are welcome!

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

[200] arXiv:2401.10151 (cross-list from math.SG) [cn-pdf, pdf, html, other]

Title: Local gluing Show Chinese title

Title: 局部粘合

Urs Frauenfelder, Joa Weber

Comments: 45 pages, 3 figures

Subjects: Symplectic Geometry (math.SG) ; Classical Analysis and ODEs (math.CA) ; Differential Geometry (math.DG) ; Dynamical Systems (math.DS) ; Geometric Topology (math.GT)