Differential Geometry

Authors and titles for September 2024

[1] arXiv:2409.00132 (cross-list from math.DG) [cn-pdf, pdf, html, other]

Title: Biconservative Surfaces in Robertson-Walker Spaces Show Chinese title

Title: 双保守曲面在罗伯特森-沃克空间中

Nurettin Cenk Turgay, Rüya Yeğin Şen

Subjects: Differential Geometry (math.DG)

[2] arXiv:2409.00321 (cross-list from math.DG) [cn-pdf, pdf, html, other]

Title: Positivity properties of the vector bundle Monge-Ampère equation Show Chinese title

Title: 向量丛蒙日-安培方程的正性性质

Aashirwad N. Ballal, Vamsi P. Pingali

Subjects: Differential Geometry (math.DG)

[3] arXiv:2409.00420 (cross-list from math.DG) [cn-pdf, pdf, html, other]

Title: Fully non-linear elliptic equations on compact hyperkähler manifolds Show Chinese title

Title: 完全非线性椭圆方程在紧致超凯勒流形上

Giovanni Gentili, Luigi Vezzoni

Comments: 14 pages

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

[4] arXiv:2409.00440 (cross-list from math.DG) [cn-pdf, pdf, html, other]

Title: $C^{1,1-ε}$ Isometric embeddings Show Chinese title

Title: $C^{1,1-ε}$等距嵌入

Ángel D. Martínez

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

[5] arXiv:2409.00462 (cross-list from math.DG) [cn-pdf, pdf, html, other]

Title: A non-Standard Indefinite Einstein Solvmanifold Show Chinese title

Title: 一个非标准的不定爱因斯坦Solvmanifold

Federico A. Rossi

Comments: 12 pages

Journal-ref: Proceedings of the International Geometry Center 18(1): 20-34 (2025)

Subjects: Differential Geometry (math.DG)

[6] arXiv:2409.00539 (cross-list from math.DG) [cn-pdf, pdf, html, other]

Title: Twistor and Reflector spaces for paraquaternionic contact manifolds Show Chinese title

Title: 扭曲空间和反射器空间对于仿四元数接触流形

Stefan Ivanov, Ivan Minchev, Marina Tchomakova

Subjects: Differential Geometry (math.DG)

[7] arXiv:2409.00583 (cross-list from math.DG) [cn-pdf, pdf, html, other]

Title: Notes on scalar curvature lower bounds of steady gradient Ricci solitons Show Chinese title

Title: 关于稳态梯度 Ricci 溶液的标量曲率下界的注记

Shota Hamanaka

Comments: 20 pages. I have made some minor modifications and removed the dimension restrictions

Subjects: Differential Geometry (math.DG)

[8] arXiv:2409.00886 (cross-list from math.DG) [cn-pdf, pdf, html, other]

Title: Continuity method for the Mabuchi soliton on the extremal Fano manifolds Show Chinese title

Title: 极小Fano流形上的Mabuchi孤立子的连续性方法

Tomoyuki Hisamoto, Satoshi Nakamura

Comments: 19 pages. The weight functions for $g$-solitons are assumed to be log-concave. Final version, to appear in Ann. Inst. Fourier (Grenoble)

Subjects: Differential Geometry (math.DG)

[9] arXiv:2409.00928 (cross-list from math.DG) [cn-pdf, pdf, html, other]

Title: Singularities of minimal submanifolds Show Chinese title

Title: 极小子流形的奇点

Leon Simon

Comments: To appear in proceedings of International Congress of Basic Science, Beijing 2024

Subjects: Differential Geometry (math.DG)

[10] arXiv:2409.01061 (cross-list from math.DG) [cn-pdf, pdf, html, other]

Title: Alexandrov sphere theorems for $ W^{2,n} $-hypersurfaces Show Chinese title

Title: 亚历山大球面定理对于$ W^{2,n} $-超曲面

Mario Santilli, Paolo Valentini

Comments: New introduction. Acknowledgments added. v3: additional material added

Subjects: Differential Geometry (math.DG)

[11] arXiv:2409.01463 (cross-list from math.DG) [cn-pdf, pdf, html, other]

Title: Revisiting generic mean curvature flow in $\mathbb{R}^3$ Show Chinese title

Title: 重新审视一般平均曲率流在$\mathbb{R}^3$中

Otis Chodosh, Kyeongsu Choi, Christos Mantoulidis, Felix Schulze

Comments: Final version. To appear in a special bicentennial issue of J. Reine Angew. Math. (Crelle)

Subjects: Differential Geometry (math.DG)

[12] arXiv:2409.01603 (cross-list from math.DG) [cn-pdf, pdf, html, other]

Title: Cuspidal edges and generalized cuspidal edges in the Lorentz-Minkowski 3-space Show Chinese title

Title: 尖点边缘和广义尖点边缘在洛伦兹-闵可夫斯基3维空间中

T. Fukui, R. Kinoshita, D. Pei, M. Umehara, H. Yu

Subjects: Differential Geometry (math.DG)

[13] arXiv:2409.01636 (cross-list from math.DG) [cn-pdf, pdf, html, other]

Title: Bi-slant Riemannian maps to Kenmotsu manifolds and some optimal inequalities Show Chinese title

Title: 双斜率黎曼映射到Kenmotsu流形及一些最优不等式

Adeeba Zaidi, Gauree Shanker

Subjects: Differential Geometry (math.DG)

[14] arXiv:2409.01734 (cross-list from math.DG) [cn-pdf, pdf, html, other]

Title: A formula for the α-Futaki character Show Chinese title

Title: α-Futaki示性式的公式

Kartick Ghosh

Comments: 14 papges, Comments are most welcome

Subjects: Differential Geometry (math.DG)

[15] arXiv:2409.01844 (cross-list from math.DG) [cn-pdf, pdf, other]

Title: Semiholonomic jets and induced modules in Cartan geometry calculus Show Chinese title

Title: 半完整芽与Cartan几何微积分中的诱导模

Jan Slovák, Vladimír Souček

Comments: 24 pages

Journal-ref: Archivum mathematicum, 60, 4 (2024), 191-219

Subjects: Differential Geometry (math.DG)

[16] arXiv:2409.01912 (cross-list from math.DG) [cn-pdf, pdf, html, other]

Title: Generalized complex Stein manifold Show Chinese title

Title: 广义复Stein流形

Debjit Pal

Comments: 49 pages, minor revision, comments are welcome

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

[17] arXiv:2409.02211 (cross-list from math.DG) [cn-pdf, pdf, html, other]

Title: Multiplicity free covering of a graded manifold Show Chinese title

Title: 无重覆盖的分次流形

Elizaveta Vishnyakova

Comments: 20 pages. Proposition 32 is corrected. Main results are unchanged. The text of the paper is reworked and simplified

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

[18] arXiv:2409.02213 (cross-list from math.DG) [cn-pdf, pdf, html, other]

Title: Isospectral spherical space forms and orbifolds of highest volume Show Chinese title

Title: 等谱球形空间形式和最高体积的轨道流形

Alfredo Álzaga, Emilio A. Lauret

Comments: Accepted in Revista de la Uni\'on Matem\'atica Argentina (February 2025)

Subjects: Differential Geometry (math.DG)

[19] arXiv:2409.02351 (cross-list from math.DG) [cn-pdf, pdf, html, other]

Title: Sobolev Metrics on Spaces of Discrete Regular Curves Show Chinese title

Title: Sobolev 度量在离散正则曲线空间上的应用

Jonathan Cerqueira (1), Emmanuel Hartman (2), Eric Klassen (1), Martin Bauer (1) ((1) Florida State University, (2) University of Houston)

Comments: 23 pages, 6 figures

Subjects: Differential Geometry (math.DG)

[20] arXiv:2409.02403 (cross-list from math.DG) [cn-pdf, pdf, html, other]

Title: Pseudo-timelike loops in signature changing semi-Riemannian manifolds with a transverse radical Show Chinese title

Title: 签名变化的半黎曼流形中伪类时序环路

N. E. Rieger, W. Hasse

Comments: Accepted for publication in Results in Physics; this version corresponds to the revised manuscript submitted to Results in Physics. 36 pages, 8 figures

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

[21] arXiv:2409.02570 (cross-list from math.DG) [cn-pdf, pdf, html, other]

Title: Ricci curvature and normalized Ricci flow on generalized Wallach spaces Show Chinese title

Title: 里奇曲率和广义瓦拉赫空间上的归一化里奇流

Nurlan Abiev

Comments: 35 pages, 13 figures, 5 tables

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

[22] arXiv:2409.02643 (cross-list from math.DG) [cn-pdf, pdf, html, other]

Title: On the Focal Locus of Submanifolds of a Finsler Manifold Show Chinese title

Title: 测地子流形的焦点轨迹

Aritra Bhowmick, Sachchidanand Prasad

Comments: 30 Pages, Comments are welcome!

Subjects: Differential Geometry (math.DG)

[23] arXiv:2409.02766 (cross-list from math.DG) [cn-pdf, pdf, html, other]

Title: Weinstock inequality in hyperbolic space Show Chinese title

Title: 魏斯托克不等式在双曲空间中

Pingxin Gu, Haizhong Li, Yao Wan

Comments: 18 pages. All comments are welcome

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

[24] arXiv:2409.02895 (cross-list from math.DG) [cn-pdf, pdf, other]

Title: A generalization of Clairaut's formula and its applications Show Chinese title

Title: 克莱罗公式的推广及其应用

Vadym Koval

Subjects: Differential Geometry (math.DG)

[25] arXiv:2409.03098 (cross-list from math.DG) [cn-pdf, pdf, html, other]

Title: Monotonicity of the modulus under curve shortening flow Show Chinese title

Title: 模的单调性在曲线缩短流下

Arjun Sobnack, Peter M. Topping

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

[26] arXiv:2409.03138 (cross-list from math.DG) [cn-pdf, pdf, html, other]

Title: From local isometries to global symmetries: Bridging Killing vectors and Lie algebras through induced vector fields Show Chinese title

Title: 从局部等距到全局对称性：通过诱导向量场连接凯尔ing向量和李代数

Thales B. S. F. Rodrigues, B. F. Rizzuti

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

[27] arXiv:2409.03314 (cross-list from math.DG) [cn-pdf, pdf, html, other]

Title: Monotonicity Formulas for Capillary Surfaces Show Chinese title

Title: 单调性公式对于毛细表面

Guofang Wang, Chao Xia, Xuwen Zhang

Subjects: Differential Geometry (math.DG)

[28] arXiv:2409.03321 (cross-list from math.DG) [cn-pdf, pdf, html, other]

Title: Willmore-type inequality in unbounded convex sets Show Chinese title

Title: 关于无界凸集的Willmore型不等式

Xiaohan Jia, Guofang Wang, Chao Xia, Xuwen Zhang

Journal-ref: J. Lond. Math. Soc. (2) 111 (2025), no. 3, Paper No. e70105, 24 pp

Subjects: Differential Geometry (math.DG)

[29] arXiv:2409.03343 (cross-list from math.DG) [cn-pdf, pdf, html, other]

Title: Almost Non-positive Kähler Manifolds Show Chinese title

Title: 几乎非正Kähler流形

Yuguang Zhang

Subjects: Differential Geometry (math.DG)

[30] arXiv:2409.03554 (cross-list from math.DG) [cn-pdf, pdf, html, other]

Title: Critical domains for certain Dirichlet integrals in weighted manifolds Show Chinese title

Title: 加权流形中某些狄利克雷积分的关键区域

Levi Lopes de Lima

Comments: Rewritten at some points to improve the presentation; Section 8 slightly expanded, became an appendix; lots of typos fixed; a few references added; 27 pages; no figures

Subjects: Differential Geometry (math.DG)

[31] arXiv:2409.03886 (cross-list from math.DG) [cn-pdf, pdf, html, other]

Title: $G_2$-instantons on the ALC members of the $\mathbb{B}_7$ family Show Chinese title

Title: $G_2$-在$\mathbb{B}_7$家族的 ALC 成员上的瞬子

Jakob Stein, Matt Turner

Comments: 23 pages, 1 figure. v2: We would like to thank an anonymous reviewer for pointing out a simpler proof of the results in section 3.6, forgoing the need for the theory of irregular singular initial value problems to parameterise asymptotic solutions to the ODE

Journal-ref: Ann Glob Anal Geom 67, 22 (2025)

Subjects: Differential Geometry (math.DG)

[32] arXiv:2409.03943 (cross-list from math.DG) [cn-pdf, pdf, html, other]

Title: On the stability of free boundary minimal submanifolds in conformal domains Show Chinese title

Title: 在共形区域中自由边界极小子流形的稳定性

Alcides de Carvalho, Roney Santos, Federico Trinca

Comments: 13 pages

Subjects: Differential Geometry (math.DG)

[33] arXiv:2409.04337 (cross-list from math.DG) [cn-pdf, pdf, html, other]

Title: Principal frequency of clamped plates on RCD(0,N) spaces: sharpness, rigidity and stability Show Chinese title

Title: 夹紧板在RCD(0,N)空间上的主频率：精确性、刚性和稳定性

Alexandru Kristály, Andrea Mondino

Comments: 30 pages

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

[34] arXiv:2409.04358 (cross-list from math.DG) [cn-pdf, pdf, html, other]

Title: The geometric Cauchy problem for constant-rank submanifolds Show Chinese title

Title: 常秩子流形的几何柯西问题

Matteo Raffaelli

Comments: 8 pages, no figures. Minor revision

Subjects: Differential Geometry (math.DG)

[35] arXiv:2409.04362 (cross-list from math.DG) [cn-pdf, pdf, html, other]

Title: Compact holonomy $\mathrm{G}_2$ manifolds need not be formal Show Chinese title

Title: 紧致全纯性$\mathrm{G}_2$流形不一定是形式的

Lucía Martín-Merchán

Comments: 15 pages. Comments welcome

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

[36] arXiv:2409.04382 (cross-list from math.DG) [cn-pdf, pdf, html, other]

Title: Local descriptions of the heterotic SU(3) moduli space Show Chinese title

Title: 杂化SU(3)模空间的局部描述

Hannah de Lázari, Jason D. Lotay, Henrique Sá Earp, Eirik Eik Svanes

Comments: v2: 34 pages, expanded introduction, example added, references updated; v3: 35 pages, new statement of the main theorem, remarks and references added, minor corrections, accepted in Comm. Math. Phys

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

[37] arXiv:2409.04426 (cross-list from math.DG) [cn-pdf, pdf, other]

Title: On minimal hypersurfaces in Euclidean spaces and Riemannian manifolds Show Chinese title

Title: 在欧几里得空间和黎曼流形中的极小超曲面

Josef Mikes, Sergey Stepanov, Irina Tsyganok

Subjects: Differential Geometry (math.DG)

[38] arXiv:2409.04460 (cross-list from math.DG) [cn-pdf, pdf, html, other]

Title: Four closed characteristics on compact star-shaped hypersurfaces in $\mathbb{R}^{8}$ Show Chinese title

Title: 四条闭合特征在紧致星形超曲面上的$\mathbb{R}^{8}$

Huagui Duan, Dong Xie

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

[39] arXiv:2409.04835 (cross-list from math.DG) [cn-pdf, pdf, html, other]

Title: Generalized paracomplex structures on generalized reflector spaces Show Chinese title

Title: 广义仿复结构在广义反射空间上

Johann Davidov

Comments: arXiv admin note: substantial text overlap with arXiv:1701.04032

Subjects: Differential Geometry (math.DG)

[40] arXiv:2409.04947 (cross-list from math.DG) [cn-pdf, pdf, html, other]

Title: Some estimates on stable minimal hypersurfaces in Euclidean space Show Chinese title

Title: 欧几里得空间中稳定极小超曲面的一些估计

Luen-Fai Tam

Comments: References have been updated

Subjects: Differential Geometry (math.DG)

[41] arXiv:2409.04956 (cross-list from math.DG) [cn-pdf, pdf, html, other]

Title: Z/2 harmonic 1-forms, R-trees, and the Morgan-Shalen compactification Show Chinese title

Title: Z/2调和1-形式，R-树和Morgan-Shalen紧化

Siqi He, Richard Wentworth, Boyu Zhang

Comments: 36 pages; added Theorem 1.3 and Corollaries 1.4, 1.5 in version 2

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

[42] arXiv:2409.05078 (cross-list from math.DG) [cn-pdf, pdf, html, other]

Title: A Note on Ricci-pinched three-manifolds Show Chinese title

Title: 关于Ricci-pinched三维流形的一篇注记

Luca Benatti, Carlo Mantegazza, Francesca Oronzio, Alessandra Pluda

Subjects: Differential Geometry (math.DG)

[43] arXiv:2409.05107 (cross-list from math.DG) [cn-pdf, pdf, html, other]

Title: Explicit formulas for the Hattori-Stong theorem and applications Show Chinese title

Title: 哈托里-斯通定理的显式公式及其应用

Ping Li, Wangyang Lin

Comments: 15 pages

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

[44] arXiv:2409.05182 (cross-list from math.DG) [cn-pdf, pdf, html, other]

Title: Universal central extension of the Lie algebra of exact divergence-free vector fields Show Chinese title

Title: 李代数的精确散度自由向量场的普遍中心扩张

Bas Janssens, Leonid Ryvkin, Cornelia Vizman

Comments: 25 pages

Subjects: Differential Geometry (math.DG)

[45] arXiv:2409.05447 (cross-list from math.DG) [cn-pdf, pdf, html, other]

Title: The bimetric spectral Einstein-Hilbert action and the Kastler-Kalau-Walze type theorem for Lorentz warped products Show Chinese title

Title: 双度规谱爱因斯坦-希尔伯特作用量和洛伦兹扭曲积的Kastler-Kalau-Walze型定理

Siyao Liu, Yong Wang

Comments: 12 pages

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

[46] arXiv:2409.05497 (cross-list from math.DG) [cn-pdf, pdf, html, other]

Title: Failure of famous functional inequalities on Finsler manifolds: the influence of $S$-curvature Show Chinese title

Title: 著名函数不等式在Finsler流形上的失效：$S$-曲率的影响

Alexandru Kristály, Benling Li, Wei Zhao

Comments: 33 pages

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

[47] arXiv:2409.05616 (cross-list from math.DG) [cn-pdf, pdf, html, other]

Title: On the Dirac spectrum on degenerating Riemannian surfaces Show Chinese title

Title: 关于退化黎曼曲面上的狄拉克谱

Cipriana Anghel

Comments: 50 pages, 8 figures

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

[48] arXiv:2409.05829 (cross-list from math.DG) [cn-pdf, pdf, other]

Title: Symplectic Reduction in Infinite Dimensions Show Chinese title

Title: 辛约化在无限维中

Tobias Diez, Gerd Rudolph

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

[49] arXiv:2409.06032 (cross-list from math.DG) [cn-pdf, pdf, html, other]

Title: On isoparametric foliations of complex and quaternionic projective spaces Show Chinese title

Title: 关于复数和四元数射影空间的等参数叶状结构

Miguel Dominguez-Vazquez, Andreas Kollross

Comments: 20 pages

Subjects: Differential Geometry (math.DG)

[50] arXiv:2409.06094 (cross-list from math.DG) [cn-pdf, pdf, html, other]

Title: Strict stability of calibrated cones Show Chinese title

Title: 校准锥的严格稳定性

Bryan Dimler, Jooho Lee

Comments: Final Version. To appear in Proc. AMS

Subjects: Differential Geometry (math.DG)