Differential Geometry

Authors and titles for January 2024

[1] arXiv:2401.00100 (cross-list from math.DG) [cn-pdf, pdf, other]

Title: Growth of spinors in the generalized Seiberg-Witten equations on $\mathbb R^4$ and $\mathbb R^3$ Show Chinese title

Title: 在$\mathbb R^4$和$\mathbb R^3$上广义 Seiberg-Witten 方程中旋量的增长

Gorapada Bera

Comments: Final version to appear in Journal of Geometry and Physics

Subjects: Differential Geometry (math.DG)

[2] arXiv:2401.00106 (cross-list from math.DG) [cn-pdf, pdf, html, other]

Title: Complete space-like self-expanders in the Minkovski space Show Chinese title

Title: 全空间类似自扩张子在闵可夫斯基空间中

Zhi Li, Guoxin Wei

Subjects: Differential Geometry (math.DG)

[3] arXiv:2401.00279 (cross-list from math.DG) [cn-pdf, pdf, html, other]

Title: Dimension of the singular set for $2$-valued stationary Lipschitz graphs Show Chinese title

Title: $2$值的平稳 Lipshitz 图的奇异集的维数

Jonas Hirsch, Luca Spolaor

Comments: Comments are welcome!

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

[4] arXiv:2401.00472 (cross-list from math.DG) [cn-pdf, pdf, html, other]

Title: On Thurston's geometrical space form problem: on quasi space forms Show Chinese title

Title: 关于汤姆森的几何空间形式问题：关于拟空间形式

Stefan Haesen, Miroslava Petrović-Torgašev, Leopold Verstraelen

Comments: 20 pages

Subjects: Differential Geometry (math.DG)

[5] arXiv:2401.00585 (cross-list from math.DG) [cn-pdf, pdf, html, other]

Title: Harmonic curvature in dimension four Show Chinese title

Title: 四维中的调和曲率

Andrzej Derdzinski

Comments: 34 pages

Journal-ref: Journal of the Korean Mathematical Society, vol. 62 (2025), no. 1, pp. 217-252

Subjects: Differential Geometry (math.DG)

[6] arXiv:2401.00606 (cross-list from math.DG) [cn-pdf, pdf, other]

Title: Backward propagation of warped product structures and asymptotically conical shrinkers Show Chinese title

Title: 扭曲乘积结构的反向传播和渐近圆锥收缩体

Brett Kotschwar

Comments: 56 pages, no figures

Subjects: Differential Geometry (math.DG)

[7] arXiv:2401.00607 (cross-list from math.DG) [cn-pdf, pdf, html, other]

Title: Ricci flows which terminate in cones Show Chinese title

Title: 在锥体中终止的里奇流

Brett Kotschwar

Comments: 52 pages, no figures

Subjects: Differential Geometry (math.DG)

[8] arXiv:2401.00709 (cross-list from math.DG) [cn-pdf, pdf, html, other]

Title: Clairaut anti-invariant Riemannian maps with Kähler and Ricci soliton structures Show Chinese title

Title: 克莱劳反不变黎曼映射与凯勒和里奇孤立子结构

Jyoti Yadav, Gauree Shanker

Comments: 25 pages

Subjects: Differential Geometry (math.DG)

[9] arXiv:2401.00720 (cross-list from math.DG) [cn-pdf, pdf, html, other]

Title: Every closed surface of genus at least 18 is Loewner Show Chinese title

Title: 每个至少18的亏格的闭曲面都是Loewner

Qiongling Li, Weixu Su

Comments: 11 pages, 1 figures. We correct an erroneous citation in previous the version

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

[10] arXiv:2401.00838 (cross-list from math.DG) [cn-pdf, pdf, html, other]

Title: Sphere-like isoparametric hypersurfaces in Damek-Ricci spaces Show Chinese title

Title: 类球面等参超曲面在Damek-Ricci空间中

Balázs Csikós, Márton Horváth

Comments: 20 pages

Subjects: Differential Geometry (math.DG)

[11] arXiv:2401.00937 (cross-list from math.DG) [cn-pdf, pdf, html, other]

Title: A fourth-order Cherrier-Escobar problem with prescribed corner behavior on the half-ball Show Chinese title

Title: 四阶 Cherrier-Escobar 问题在半球上具有预定角行为

Jeffrey S. Case, Yueh-Ju Lin, Stephen E. McKeown, Cheikh Birahim Ndiaye, Paul Yang

Comments: 28 pages

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

[12] arXiv:2401.00946 (cross-list from math.DG) [cn-pdf, pdf, other]

Title: Non-contractible closed geodesics on compact Finsler space forms without self-intersections Show Chinese title

Title: 不可缩的闭测地线在没有自交的紧致芬斯勒空间形式上

Yuchen Wang

Comments: arXiv admin note: text overlap with arXiv:2202.10004

Subjects: Differential Geometry (math.DG) ; Dynamical Systems (math.DS)

[13] arXiv:2401.01153 (cross-list from math.DG) [cn-pdf, pdf, html, other]

Title: Quantization of the Kähler-Ricci flow and optimal destabilizer for a Fano manifold Show Chinese title

Title: Kähler-Ricci流的量化和Fano流形的最优不稳定化

Tomoyuki Hisamoto

Subjects: Differential Geometry (math.DG)

[14] arXiv:2401.01338 (cross-list from math.DG) [cn-pdf, pdf, html, other]

Title: Equivariant Morse theory for Lie algebra actions on Riemannian foliations Show Chinese title

Title: 李代数在黎曼叶状结构上的等变莫尔斯理论

Yi Lin, Zuoqin Wang

Comments: 36 pages. Comments welcome

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

[15] arXiv:2401.01492 (cross-list from math.DG) [cn-pdf, pdf, html, other]

Title: Stable minimal hypersurfaces in $\mathbf{R}^5$ Show Chinese title

Title: 稳定极小超曲面在$\mathbf{R}^5$中

Otis Chodosh, Chao Li, Paul Minter, Douglas Stryker

Subjects: Differential Geometry (math.DG)

[16] arXiv:2401.01535 (cross-list from math.DG) [cn-pdf, pdf, html, other]

Title: Formal manifolds: foundations Show Chinese title

Title: 形式流形：基础

Fulin Chen, Binyong Sun, Chuyun Wang

Comments: First version of this paper was split into three separate papers. Vector-valued generalized functions and vector-valued distributions were separated into "Function spaces on Formal Manifolds" preprint, while de Rham complexes and Poincare's Lemma were separated into "Poincare's Lemma for formal manifolds"preprint. All the rest about the foundations of formal manifolds stayed in v3 of this preprint

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

[17] arXiv:2401.01688 (cross-list from math.DG) [cn-pdf, pdf, html, other]

Title: Complete Geodesic Metrics in Big Classes Show Chinese title

Title: 完整测地度量在大类中

Prakhar Gupta

Comments: 33 pages, comments are welcome

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

[18] arXiv:2401.02060 (cross-list from math.DG) [cn-pdf, pdf, other]

Title: Noncompact $n$-dimensional Einstein spaces as attractors for the Einstein flow Show Chinese title

Title: 非紧致$n$维爱因斯坦空间作为爱因斯坦流的吸引子

Jinhua Wang

Comments: 53 pages

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

[19] arXiv:2401.02087 (cross-list from math.DG) [cn-pdf, pdf, html, other]

Title: Green functions for GJMS operators on spheres, Gegenbauer polynomials and rigidity theorems Show Chinese title

Title: GJMS算子在球面上的格林函数，Gegenbauer多项式和刚性定理

Xuezhang Chen, Yalong Shi

Comments: 41 pages, no figures. Using the Positive Mass Theorem, we prove a strong rigidity theorem in dimension 3,4,5. Other parts remain the same. Comments are welcome!

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

[20] arXiv:2401.02136 (cross-list from math.DG) [cn-pdf, pdf, html, other]

Title: $L^p$-spectral theory for the Laplacian on forms Show Chinese title

Title: $L^p$-微分形式上的拉普拉斯算子的谱理论

Nelia Charalambous, Zhiqin Lu

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

[21] arXiv:2401.02228 (cross-list from math.DG) [cn-pdf, pdf, other]

Title: Infinite-Time Singularities of the Lagrangian Mean Curvature Flow Show Chinese title

Title: 无限时间的拉格朗日平均曲率流的奇点

Wei-Bo Su, Chung-Jun Tsai, Albert Wood

Comments: minor modifications; add a precise polynomial blow-up rate of the second fundamental form

Subjects: Differential Geometry (math.DG)

[22] arXiv:2401.02503 (cross-list from math.DG) [cn-pdf, pdf, html, other]

Title: On post-Lie algebras structures coming from simply transitive NIL-affine actions Show Chinese title

Title: 从单侧传递 NIL-仿射作用中产生的后李代数结构

Jonas Deré, Marcos Origlia

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

[23] arXiv:2401.02655 (cross-list from math.DG) [cn-pdf, pdf, html, other]

Title: CscK metrics near the canonical class Show Chinese title

Title: CscK 度量在典范类附近

Bin Guo, Wangjian Jian, Yalong Shi, Jian Song

Comments: 13 pages, no figures. All comments are welcome!

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

[24] arXiv:2401.02685 (cross-list from math.DG) [cn-pdf, pdf, html, other]

Title: The dimension of polynomial growth holomorphic functions and forms on gradient Kähler Ricci shrinkers Show Chinese title

Title: 梯度Kähler Ricci收缩上的多项式增长全纯函数和形式的维数

Fei He, Jianyu Ou

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

[25] arXiv:2401.02724 (cross-list from math.DG) [cn-pdf, pdf, other]

Title: Topology of the Dirac equation on spectrally large three-manifolds Show Chinese title

Title: 狄拉克方程在谱大三维流形上的拓扑结构

Francesco Lin

Comments: 25 pages, comments are welcome

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

[26] arXiv:2401.02752 (cross-list from math.DG) [cn-pdf, pdf, html, other]

Title: Characterization of Sasakian manifolds Show Chinese title

Title: Sasakian流形的特征

Vladimir Rovenski

Comments: 14 pages. In this paper, we continue our study arXiv:2312.11411

Subjects: Differential Geometry (math.DG)

[27] arXiv:2401.02768 (cross-list from math.DG) [cn-pdf, pdf, html, other]

Title: Gauss Curvature Flow on Surfaces of Revolution -- The Noncompact Case Show Chinese title

Title: 旋转曲面上的高斯曲率流——非紧情形

Thalia D. Jeffres, Leonardo Solanilla

Subjects: Differential Geometry (math.DG)

[28] arXiv:2401.02805 (cross-list from math.DG) [cn-pdf, pdf, html, other]

Title: Riemannian Geometry of $G_2$-type Real Flag Manifolds Show Chinese title

Title: 黎曼几何的$G_2$型实旗形流形

Brian Grajales, Gabriel Rondón, Julieth Saavedra

Comments: 29 pages, 4 figures

Subjects: Differential Geometry (math.DG) ; Dynamical Systems (math.DS)

[29] arXiv:2401.02910 (cross-list from math.DG) [cn-pdf, pdf, html, other]

Title: Kähler metrics and toric Lagrangian fibrations Show Chinese title

Title: 凯勒度量和环面拉格朗日纤维化

Rui Loja Fernandes, Maarten Mol

Comments: 58 pages. Comments welcomed!

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

[30] arXiv:2401.03029 (cross-list from math.DG) [cn-pdf, pdf, html, other]

Title: Symplectic geometry of Teichmüller spaces for surfaces with ideal boundary Show Chinese title

Title: 辛几何的曲面理想边界Teichmüller空间

Anton Alekseev, Eckhard Meinrenken

Comments: 48 pages, 2 figures

Journal-ref: Commun. Math. Phys. (2024) 405:229

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

[31] arXiv:2401.03034 (cross-list from math.DG) [cn-pdf, pdf, html, other]

Title: Lie Algebroids Show Chinese title

Title: 李代数胚

Eckhard Meinrenken

Comments: 10 pages, overview article for the Encyclopedia of Mathematical Physics

Journal-ref: Encyclopedia of Mathematical Physics (Second Edition) Volume 4, 2025, Pages 485-492

Subjects: Differential Geometry (math.DG)

[32] arXiv:2401.03273 (cross-list from math.DG) [cn-pdf, pdf, html, other]

Title: Recent development in biconservative submanifolds Show Chinese title

Title: 双保守子流形的最新发展

Bang-Yen Chen

Comments: 49 pages

Subjects: Differential Geometry (math.DG)

[33] arXiv:2401.03292 (cross-list from math.DG) [cn-pdf, pdf, html, other]

Title: Geometry and topology of maximal antipodal sets and related topics Show Chinese title

Title: 极大对径集的几何与拓扑及相关主题

Bang-Yen Chen

Comments: 25 pages

Journal-ref: Romanian Journal of Mathematics and Computer Science, 2023

Subjects: Differential Geometry (math.DG) ; Combinatorics (math.CO)

[34] arXiv:2401.03332 (cross-list from math.DG) [cn-pdf, pdf, html, other]

Title: Generalized Ricci flow on aligned homogeneous spaces Show Chinese title

Title: 对齐齐次空间上的广义里奇流

Valeria Gutiérrez

Journal-ref: Proceedings of the Edinburgh Mathematical Society 68 (2025) 226-246

Subjects: Differential Geometry (math.DG)

[35] arXiv:2401.03387 (cross-list from math.DG) [cn-pdf, pdf, html, other]

Title: On noncollapsed $\mathbb{F}$-limit metric solitons Show Chinese title

Title: 关于非坍缩$\mathbb{F}$-极限度量孤立子

Pak-Yeung Chan, Zilu Ma, Yongjia Zhang

Subjects: Differential Geometry (math.DG)

[36] arXiv:2401.03394 (cross-list from math.DG) [cn-pdf, pdf, html, other]

Title: Liouville theorem for minimal graphs over manifolds of nonnegative Ricci curvature Show Chinese title

Title: 黎曼流形非负里奇曲率上的极小图的刘维尔定理

Qi Ding

Comments: 14 pages

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

[37] arXiv:2401.03417 (cross-list from math.DG) [cn-pdf, pdf, html, other]

Title: Regularity of the geodesic flow on submanifolds Show Chinese title

Title: 测地流在子流形上的正则性

Christian Lange

Comments: 10 pages

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

[38] arXiv:2401.03442 (cross-list from math.DG) [cn-pdf, pdf, html, other]

Title: An Index III lemma and Rauch III theorem & applications Show Chinese title

Title: 一个III型引理和Rauch III定理及应用

Shengqi Hu, Xiaole Su, Yusheng Wang

Comments: 9 pages

Subjects: Differential Geometry (math.DG)

[39] arXiv:2401.03457 (cross-list from math.DG) [cn-pdf, pdf, html, other]

Title: Obstructions to prescribed Q-curvature of complete conformal metric on $\mathbb{R}^n$ Show Chinese title

Title: 完全共形度量在$\mathbb{R}^n$上的预定 Q 曲率的障碍

Mingxiang Li

Comments: 20 pages. All comments are welcome!

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

[40] arXiv:2401.03758 (cross-list from math.DG) [cn-pdf, pdf, html, other]

Title: Berry phases and connection matrices defined on homogeneous spaces attached to Siegel-Jacobi groups Show Chinese title

Title: 贝里相位和在与塞格尔-雅可比群相关的齐性空间上定义的连接矩阵

Stefan Berceanu

Comments: 49 pages, Latex, amsart, AMS fonts

Subjects: Differential Geometry (math.DG)

[41] arXiv:2401.03909 (cross-list from math.DG) [cn-pdf, pdf, other]

Title: The gap phenomenon for conformally related Einstein metrics Show Chinese title

Title: 共形相关的爱因斯坦度量的间隙现象

Jan Gregorovič, Josef Šilhan

Comments: 14 pages

Subjects: Differential Geometry (math.DG)

[42] arXiv:2401.03935 (cross-list from math.DG) [cn-pdf, pdf, html, other]

Title: Continuity of solutions to complex Monge-Ampère equations on compact Kähler spaces Show Chinese title

Title: 紧Kähler空间上复Monge-Ampère方程解的连续性

Ye-Won Luke Cho, Young-Jun Choi

Comments: 20 pages. Comments are welcome. The final version is to appear in Math. Ann

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

[43] arXiv:2401.04031 (cross-list from math.DG) [cn-pdf, pdf, other]

Title: Periodic Polyhedra in Spaces of Constant Curvature Show Chinese title

Title: 常曲率空间中的周期性多面体

Christina Duffield, Daniel Freese, William Holt, Matthias Weber, Ramazan Yol

Comments: 37 pages, 80 figures

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

[44] arXiv:2401.04544 (cross-list from math.DG) [cn-pdf, pdf, html, other]

Title: A Lefschetz fixed-point formula for noncompact fixed-point sets Show Chinese title

Title: 一个非紧固定点集的Lefschetz不动点公式

Peter Hochs

Comments: 33 pages

Subjects: Differential Geometry (math.DG) ; K-Theory and Homology (math.KT) ; Operator Algebras (math.OA)

[45] arXiv:2401.04548 (cross-list from math.DG) [cn-pdf, pdf, html, other]

Title: Generalised Killing Spinors on Three-Dimensional Lie Groups Show Chinese title

Title: 三维李群上的广义Killing旋量

Diego Artacho

Comments: To appear in Manuscripta Mathematica. Incorporated suggestions from anonymous referees

Journal-ref: manuscripta math. 176, 15 (2025)

Subjects: Differential Geometry (math.DG) ; Representation Theory (math.RT)

[46] arXiv:2401.04721 (cross-list from math.DG) [cn-pdf, pdf, other]

Title: Helicoidal surfaces of prescribed mean curvature in $\mathbb{R}^3$ Show Chinese title

Title: 螺旋面在$\mathbb{R}^3$中的给定平均曲率

Aires Eduardo Menani Barbieri

Comments: 27 pages, 18 figures. arXiv admin note: text overlap with arXiv:1902.09405 by other authors

Subjects: Differential Geometry (math.DG)

[47] arXiv:2401.04743 (cross-list from math.DG) [cn-pdf, pdf, html, other]

Title: Optimal matching between curves in a manifold Show Chinese title

Title: 流形中曲线之间的最优匹配

Alice Le Brigant (SAMM), Marc Arnaudon (IMB), Frédéric Barbaresco

Comments: arXiv admin note: substantial text overlap with arXiv:1703.05107

Journal-ref: Geometric Science of Information 2017, 2017, Paris, France

Subjects: Differential Geometry (math.DG)

[48] arXiv:2401.04983 (cross-list from math.DG) [cn-pdf, pdf, html, other]

Title: The Funk-Finsler structure on the unit disc in the hyperbolic plane Show Chinese title

Title: 双曲平面上单位圆盘上的Funk-Finsler结构

Ashok Kumar, Hemangi Madhusudan Shah, Bankteshwar Tiwari

Subjects: Differential Geometry (math.DG)

[49] arXiv:2401.05028 (cross-list from math.DG) [cn-pdf, pdf, html, other]

Title: Three-dimensional positively curved generalized Ricci solitons with SO(3)-symmetries Show Chinese title

Title: 三维正曲率广义里奇孤立子与SO(3)对称性

Fabio Podestà, Alberto Raffero

Journal-ref: Advances in Mathematics, 479, 110426, 2025

Subjects: Differential Geometry (math.DG)

[50] arXiv:2401.05056 (cross-list from math.DG) [cn-pdf, pdf, html, other]

Title: A discrete uniformization theorem for decorated piecewise hyperbolic metrics on surfaces Show Chinese title

Title: 曲面上传递的装饰分片双曲度量的离散统一定理

Xu Xu, Chao Zheng

Comments: arXiv admin note: text overlap with arXiv:2308.02271

Subjects: Differential Geometry (math.DG)