Differential Geometry

Authors and titles for July 2024

[1] arXiv:2407.00094 (cross-list from math.DG) [cn-pdf, pdf, html, other]

Title: Berwald $m$-Kropina Spaces of Arbitrary Signature: Metrizability and Ricci-Flatness Show Chinese title

Title: 伯威尔德$m$-克普林空间的任意符号：可度量化性和里奇平坦性

Sjors Heefer

Journal-ref: J. Math. Phys. 65, 122502 (2024)

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

[2] arXiv:2407.00169 (cross-list from math.DG) [cn-pdf, pdf, html, other]

Title: On Relative Cohomology in Lie Theory Show Chinese title

Title: 关于李理论中的相对上同调

Maria Amelia Salazar

Subjects: Differential Geometry (math.DG)

[3] arXiv:2407.00770 (cross-list from math.DG) [cn-pdf, pdf, html, other]

Title: Quantitative tightness for three-dimensional contact manifolds: a sub-Riemannian approach Show Chinese title

Title: 三维接触流形的定量紧性：一种次黎曼方法

Andrei A. Agrachev, Stefano Baranzini, Eugenio Bellini, Luca Rizzi

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

[4] arXiv:2407.00831 (cross-list from math.DG) [cn-pdf, pdf, other]

Title: Symplectic double groupoids and the generalized Kähler potential Show Chinese title

Title: 辛对称双群胚与广义的凯勒势

Daniel Álvarez, Marco Gualtieri, Yucong Jiang

Comments: 58 pages

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

[5] arXiv:2407.01062 (cross-list from math.DG) [cn-pdf, pdf, html, other]

Title: Planar closed curves with prescribed curvature Show Chinese title

Title: 平面闭曲线的给定曲率

Paolo Caldiroli, Anna Capietto

Comments: 13 pages

Journal-ref: Discrete and Continuous Dynamical Systems, 2024, 44(10): 3209-3221

Subjects: Differential Geometry (math.DG)

[6] arXiv:2407.01150 (cross-list from math.DG) [cn-pdf, pdf, html, other]

Title: Degenerating conic Kähler-Einstein metrics to the normal cone Show Chinese title

Title: 退化圆锥凯勒-爱因斯坦度量到法线锥

Olivier Biquard, Henri Guenancia

Comments: 71 pages, v2: final version, to appear in Geometry & Topology

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

[7] arXiv:2407.01166 (cross-list from math.DG) [cn-pdf, pdf, html, other]

Title: Spinc structures on real Bott manifolds Show Chinese title

Title: 实Bott流形上的旋量结构

Anna Gąsior, Rafał Lutowski

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

[8] arXiv:2407.01170 (cross-list from math.DG) [cn-pdf, pdf, html, other]

Title: Geometric singularities and Hodge theory Show Chinese title

Title: 几何奇点与霍奇理论

Lashi Bandara, Georges Habib

Comments: Added examples of rough metrics; Simplified proof of Proposition A.14

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

[9] arXiv:2407.01240 (cross-list from math.DG) [cn-pdf, pdf, html, other]

Title: Self-shrinkers whose asymptotic cones fatten Show Chinese title

Title: 自身收缩的其渐近锥体变粗

Daniel Ketover

Comments: Added additional references to recent related work

Subjects: Differential Geometry (math.DG)

[10] arXiv:2407.01427 (cross-list from math.DG) [cn-pdf, pdf, html, other]

Title: Bundle type sub-Riemannian structures on holonomy bundles Show Chinese title

Title: 横截联络在全纯性丛上的分量类型子黎曼结构

Eder M. Correa, Giovane Galindo, Lino Grama

Comments: 13 pages, Comments are welcome

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

[11] arXiv:2407.01508 (cross-list from math.DG) [cn-pdf, pdf, html, other]

Title: Mapping Cone Connections and their Yang-Mills Functional Show Chinese title

Title: 映射锥连接及其杨-米尔斯泛函

Li-Sheng Tseng, Jiawei Zhou

Comments: 36 pages. This paper is an outgrowth of arXiv:2210.03032 which will be split into two papers. This work focus on the cone Yang-Mills functional. The other that will replace the original will concern the primitive Yang-Mills functional. v2: Minor revisions and clarifications. v3: Published version

Journal-ref: Commun. Math. Phys. 406 (2025) 156

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

[12] arXiv:2407.01729 (cross-list from math.DG) [cn-pdf, pdf, html, other]

Title: Deformations of curves with constant curvature Show Chinese title

Title: 曲线的变形与恒定曲率

Mohammad Ghomi, Matteo Raffaelli

Comments: 14 pages, 2 figures; Typos corrected

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

[13] arXiv:2407.01871 (cross-list from math.DG) [cn-pdf, pdf, html, other]

Title: Mabuchi Kähler solitons versus extremal Kähler metrics and beyond Show Chinese title

Title: Mabuchi Kähler 孤子与极值 Kähler 度量及更广泛的领域

Vestislav Apostolov, Abdellah Lahdili, Yasufumi Nitta

Comments: final version, to appear in Bull. London Math. Soc

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

[14] arXiv:2407.02041 (cross-list from math.DG) [cn-pdf, pdf, html, other]

Title: Logarithmic systolic growth for hyperbolic surfaces in every genus Show Chinese title

Title: 双曲曲面在每种亏格中的对数同步增长

Mikhail G. Katz, Stephane Sabourau

Comments: 8 pages. To appear in Proceedings of the American Mathematical Society

Subjects: Differential Geometry (math.DG)

[15] arXiv:2407.02189 (cross-list from math.DG) [cn-pdf, pdf, html, other]

Title: SKT solvable Lie algebras with codimension two nilradical Show Chinese title

Title: 具有二维余维幂零根的SKT可解李代数

Beatrice Brienza, Anna Fino

Comments: 27 pages

Subjects: Differential Geometry (math.DG)

[16] arXiv:2407.02296 (cross-list from math.DG) [cn-pdf, pdf, html, other]

Title: Sard properties for polynomial maps in infinite dimension Show Chinese title

Title: 无限维中多项式映射的Sard性质

Antonio Lerario, Luca Rizzi, Daniele Tiberio

Comments: 39 pages. V2: improved presentation, some of the main results have been tweaked

Subjects: Differential Geometry (math.DG) ; Functional Analysis (math.FA) ; Metric Geometry (math.MG) ; Optimization and Control (math.OC)

[17] arXiv:2407.02332 (cross-list from math.DG) [cn-pdf, pdf, html, other]

Title: Li-Yau Conformal Volume and Colding-Minicozzi Entropy of Self-Shrinkers Show Chinese title

Title: Li-Yau共形体积和自缩影的Colding-Minicozzi熵

Jacob Bernstein

Comments: 28 pages

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

[18] arXiv:2407.02334 (cross-list from math.DG) [cn-pdf, pdf, html, other]

Title: Quasiregular curves: Removability of singularities Show Chinese title

Title: 拟正则曲线：奇点的可去除性

Toni Ikonen

Comments: 19 pages; added an injectivity radius lower bound assumption to the results about manifold-valued curves; contains a new section connecting injectivity radius lower bound and sectional curvature upper bound to isoperimetric inequalities up to small mass

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

[19] arXiv:2407.02607 (cross-list from math.DG) [cn-pdf, pdf, other]

Title: Product Geometries on Cholesky Manifolds with Applications to SPD Manifolds Show Chinese title

Title: Cholesky流形上的乘积几何及其在对称正定流形中的应用

Ziheng Chen, Yue Song, Xiao-Jun Wu, Nicu Sebe

Comments: 25 pages, 1 figures

Subjects: Differential Geometry (math.DG) ; Machine Learning (cs.LG) ; Metric Geometry (math.MG)

[20] arXiv:2407.02875 (cross-list from math.DG) [cn-pdf, pdf, html, other]

Title: The structure of deformed double complexes on the Iwasawa manifold Show Chinese title

Title: 在Iwasawa流形上的变形双复形结构

Yan Hu, Wei Xia

Comments: 26 pages

Subjects: Differential Geometry (math.DG)

[21] arXiv:2407.02905 (cross-list from math.DG) [cn-pdf, pdf, html, other]

Title: Geodesic loops and orthogonal geodesic chords without self-intersections Show Chinese title

Title: 测地线环和无自相交的正交测地线弦

Hans-Bert Rademacher

Comments: 17 pages. Following the suggestions of the referee the Introduction has been extended and a few non-mathematical changes have been made

Subjects: Differential Geometry (math.DG)

[22] arXiv:2407.03095 (cross-list from math.DG) [cn-pdf, pdf, html, other]

Title: Conformally homogeneous Lorentzian spaces Show Chinese title

Title: 共形齐次洛伦兹空间

Dmitri V. Alekseevsky, Anton S. Galaev

Comments: 16 pages; the final version accepted for publication in Communications in Contemporary Mathematics

Subjects: Differential Geometry (math.DG)

[23] arXiv:2407.03127 (cross-list from math.DG) [cn-pdf, pdf, html, other]

Title: Flows of SU(2)-structures Show Chinese title

Title: SU(2)-结构的流形

Udhav Fowdar, Henrique N. Sá Earp

Comments: 40 pages, to appear in Math. Z

Subjects: Differential Geometry (math.DG)

[24] arXiv:2407.03193 (cross-list from math.DG) [cn-pdf, pdf, html, other]

Title: Tian's theorem for Moishezon spaces Show Chinese title

Title: 天定理对于Moishezon空间

Dan Coman, Xiaonan Ma, George Marinescu

Comments: 10 pages; v.2 is a final update to agree with the published paper

Journal-ref: Rev. Roumaine Math. Pures Appl. 69 (2024), 3-4, 433-444

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

[25] arXiv:2407.03222 (cross-list from math.DG) [cn-pdf, pdf, html, other]

Title: On $δ$-Stable Minimal Hypersurfaces in $\mathbb{R}^{n+1}$ Show Chinese title

Title: 关于$δ$稳定的最小超曲面在$\mathbb{R}^{n+1}$中

Han Hong, Haizhong Li, Gaoming Wang

Comments: 37 pages. Comments are welcome

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

[26] arXiv:2407.03246 (cross-list from math.DG) [cn-pdf, pdf, html, other]

Title: Moment maps and stability of holomorphic submersions Show Chinese title

Title: 矩映射和全纯子明映射的稳定性

Annamaria Ortu

Comments: v2: 28 pages. Clarifies the case of obstructed deformations

Subjects: Differential Geometry (math.DG)

[27] arXiv:2407.03306 (cross-list from math.DG) [cn-pdf, pdf, html, other]

Title: Duals of Higher Vector Spaces Show Chinese title

Title: 高维向量空间的对偶性

Stefano Ronchi, Chenchang Zhu

Comments: 46 pages, preliminary version, comments are welcome!

Subjects: Differential Geometry (math.DG) ; Algebraic Topology (math.AT) ; Category Theory (math.CT)

[28] arXiv:2407.03529 (cross-list from math.DG) [cn-pdf, pdf, html, other]

Title: Geometric and Analytic Aspects of Simon-Lojasiewicz Inequalities on Vector Bundles Show Chinese title

Title: 向量丛上的西蒙-洛瓦斯iewicz不等式的几何与分析方面

Owen Drummond

Comments: 21 pages, 4 figures

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

[29] arXiv:2407.03534 (cross-list from math.DG) [cn-pdf, pdf, html, other]

Title: Myers-Steenrod theorems for metric and singular Riemannian foliations Show Chinese title

Title: Myers-Steenrod 定理对于度量和奇异黎曼叶状结构

Diego Corro, Fernando Galaz-García

Comments: 20 pages, we thank gold essen.trinken in Karlsruhe for its excellent working conditions

Subjects: Differential Geometry (math.DG)

[30] arXiv:2407.03693 (cross-list from math.DG) [cn-pdf, pdf, html, other]

Title: Multi-toric geometries with larger compact symmetry Show Chinese title

Title: 具有更大紧致对称性的多环面几何结构

Thomas Bruun Madsen, Andrew Swann

Comments: 19 pages

Subjects: Differential Geometry (math.DG)

[31] arXiv:2407.03803 (cross-list from math.DG) [cn-pdf, pdf, html, other]

Title: Extending Gromov's optimal systolic inequality Show Chinese title

Title: 扩展格罗莫夫的最佳系统不等式

Thomas G. Goodwillie, James J. Hebda, Mikhail G. Katz

Comments: 8 pages, published in Journal of Geometry

Journal-ref: Journal of Geometry 114 (2023), article 23

Subjects: Differential Geometry (math.DG)

[32] arXiv:2407.03855 (cross-list from math.DG) [cn-pdf, pdf, html, other]

Title: On Riemann curvature of spherically symmetric metrics Show Chinese title

Title: 球对称度量的黎曼曲率

S.G. Elgendi

Comments: Accepted for publication in Mathematical Physics, Analysis and Geometry

Subjects: Differential Geometry (math.DG)

[33] arXiv:2407.03989 (cross-list from math.DG) [cn-pdf, pdf, html, other]

Title: Foliations transverse to a closed conformal vector field Show Chinese title

Title: 与闭合共形向量场正交的叶状结构

Euripedes da Silva, Ícaro Gonçalves, Júlio Pereira

Comments: 15 pages, 2 figures

Subjects: Differential Geometry (math.DG)

[34] arXiv:2407.04131 (cross-list from math.DG) [cn-pdf, pdf, html, other]

Title: Ends of (singular) Ricci shrinkers Show Chinese title

Title: 奇异Ricci缩引的端点

Alessandro Bertellotti, Reto Buzano

Comments: V2: Final version with minor revisions. To appear in Selecta Math

Subjects: Differential Geometry (math.DG)

[35] arXiv:2407.04310 (cross-list from math.DG) [cn-pdf, pdf, html, other]

Title: Connection matrices on the Siegel-Jacobi upper half space and extended Siegel-Jacobi upper half space Show Chinese title

Title: 塞格尔-雅可比上半空间和扩展塞格尔-雅可比上半空间上的连接矩阵

Elena Mirela Babalic, Stefan Berceanu

Comments: 18 pages

Subjects: Differential Geometry (math.DG)

[36] arXiv:2407.04421 (cross-list from math.DG) [cn-pdf, pdf, html, other]

Title: On the classificarion of 3-dimensional spherical Sasakian manifolds Show Chinese title

Title: 关于三维球面Sasakian流形的分类

Daniel Sykes, Gerd Schmalz, Vladimir Ezhov

Journal-ref: Izv. Math. 85 (2021), no. 3, 518-528

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

[37] arXiv:2407.04539 (cross-list from math.DG) [cn-pdf, pdf, html, other]

Title: Nijenhuis geometry of parallel tensors Show Chinese title

Title: 平行张量的Nijenhuis几何

Andrzej Derdzinski, Paolo Piccione, Ivo Terek

Comments: Further typos corrected, text streamlined in places, some references added

Journal-ref: Annali di Matematica Pura ed Applicata (2024), OnlineFirst

Subjects: Differential Geometry (math.DG)

[38] arXiv:2407.04623 (cross-list from math.DG) [cn-pdf, pdf, html, other]

Title: Balanced metrics and Gauduchon cone of locally conformally Kahler manifolds Show Chinese title

Title: 平衡度量与局部共形凯勒流形的高斯通锥

Liviu Ornea, Misha Verbitsky

Comments: 17 pages, version 2.0, added reference Alexandrov-Ivanov, to Dinew-Popovici and Arroyo-Nicolini

Subjects: Differential Geometry (math.DG)

[39] arXiv:2407.04786 (cross-list from math.DG) [cn-pdf, pdf, html, other]

Title: Sharpening a gap theorem: nonnegative Ricci and small curvature concentration Show Chinese title

Title: 加强一个间隙定理：非负 Ricci 曲率和小曲率集中

Adam Martens

Comments: To appear in Calculus of Variations and Partial Differential Equations. Final version

Subjects: Differential Geometry (math.DG)

[40] arXiv:2407.04851 (cross-list from math.DG) [cn-pdf, pdf, html, other]

Title: Time geodesics on a slippery cross slope under gravitational wind Show Chinese title

Title: 重力风作用下滑腻横坡上的时间测地线

Nicoleta Aldea, Piotr Kopacz

Comments: 30 pages, 11 figures, to appear in Nonlinear Analysis - Real World Applications

Journal-ref: Nonlinear Analysis: Real World Applications 81, 104177 (2025)

Subjects: Differential Geometry (math.DG)

[41] arXiv:2407.04946 (cross-list from math.DG) [cn-pdf, pdf, html, other]

Title: Boundary determination of the Riemannian metric by the elastic Dirichlet-to-Neumann map Show Chinese title

Title: 黎曼度量的边界由弹性狄利克雷-诺伊曼映射确定

Xiaoming Tan

Comments: 11 pages

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

[42] arXiv:2407.05188 (cross-list from math.DG) [cn-pdf, pdf, html, other]

Title: Comparison of the Hitchin metric and the semi-flat metric in the rank two case Show Chinese title

Title: 二阶情况下的Hitchin度量与半平坦度量的比较

Takuro Mochizuki

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

[43] arXiv:2407.05274 (cross-list from math.DG) [cn-pdf, pdf, html, other]

Title: Weyls's law for Compact Rank One Symmetric Spaces Show Chinese title

Title: 魏尔兹的定律对于紧致的一阶对称空间

Anupam Pal Choudhury, Sai Sriharsha Indukuri, Ritwik Mukherjee

Comments: 16 pages. Comments are welcome

Subjects: Differential Geometry (math.DG)

[44] arXiv:2407.05406 (cross-list from math.DG) [cn-pdf, pdf, html, other]

Title: Complete minimal hypersurfaces in a hyperbolic space $H^{4}(-1)$ Show Chinese title

Title: 完备的双曲空间中的极小超曲面 $H^{4}(-1)$

Qing-Ming Cheng, Yejuan Peng

Comments: 17pages

Subjects: Differential Geometry (math.DG)

[45] arXiv:2407.05513 (cross-list from math.DG) [cn-pdf, pdf, html, other]

Title: Blow-ups of minimal surfaces in the Heisenberg group Show Chinese title

Title: 在Heisenberg群中的极小曲面的爆破

Yonghao Yu

Subjects: Differential Geometry (math.DG)

[46] arXiv:2407.05515 (cross-list from math.DG) [cn-pdf, pdf, html, other]

Title: Magnetic trajectories on Heisenberg nilmanifolds Show Chinese title

Title: Heisenberg 纹波流形上的磁轨迹

Gabriela P. Ovando, Mauro Subils

Comments: 37 pages including two pages of appendix

Subjects: Differential Geometry (math.DG)

[47] arXiv:2407.05574 (cross-list from math.DG) [cn-pdf, pdf, html, other]

Title: Complete Riemannian 4-manifolds with uniformly positive scalar curvature Show Chinese title

Title: 具有均匀正标量曲率的完备黎曼4-流形

Otis Chodosh, Davi Maximo, Anubhav Mukherjee

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

[48] arXiv:2407.05602 (cross-list from math.DG) [cn-pdf, pdf, html, other]

Title: Sharp Interior Gradient Estimate for Area Decreasing Graphical Mean Curvature Flow in Arbitrary Codimension Show Chinese title

Title: 任意余维下面积递减图形式均值曲率流的尖锐内部梯度估计

Jingbo Wan

Comments: 21 pages, comments are welcome!

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

[49] arXiv:2407.05660 (cross-list from math.DG) [cn-pdf, pdf, html, other]

Title: Manifolds with non-positive second Chern-Ricci curvature Show Chinese title

Title: 具有非正第二陈-里奇曲率的流形

Xiaokui Yang

Subjects: Differential Geometry (math.DG)

[50] arXiv:2407.05661 (cross-list from math.DG) [cn-pdf, pdf, html, other]

Title: On the stability of Killing cylinders in hyperbolic space Show Chinese title

Title: 论双曲空间中Killing圆柱的稳定性

Antonio Bueno, Rafael López

Comments: 8 figures. Accepted for publication in Journal of Geometric Analysis

Subjects: Differential Geometry (math.DG)