Umbilicity and the First Stability Eigenvalue of a Subclass of CMC Hypersurfaces Immersed in Certain Einstein Manifolds

IF 0.9 3区 数学 Q3 MATHEMATICS, APPLIED Mathematical Physics, Analysis and Geometry Pub Date : 2025-02-03 DOI:10.1007/s11040-025-09499-y
Henrique F. de Lima, Ary V. F. Leite, Marco Antonio L. Velásquez
{"title":"Umbilicity and the First Stability Eigenvalue of a Subclass of CMC Hypersurfaces Immersed in Certain Einstein Manifolds","authors":"Henrique F. de Lima,&nbsp;Ary V. F. Leite,&nbsp;Marco Antonio L. Velásquez","doi":"10.1007/s11040-025-09499-y","DOIUrl":null,"url":null,"abstract":"<div><p>We study the umbilicity of constant mean curvature (CMC) complete hypersurfaces immersed in an Einstein manifold satisfying appropriate curvature constraints. In this setting, we obtain new characterization results for totally umbilical hypersurfaces via suitable maximum principles which deal with the notions of convergence to zero at infinity and polynomial volume growth. Afterwards, we establish optimal estimates for the first eigenvalue of the stability operator of CMC compact hypersurfaces in such an Einstein manifold. In particular, we derive a nonexistence result concerning strongly stable CMC hypersurfaces.</p></div>","PeriodicalId":694,"journal":{"name":"Mathematical Physics, Analysis and Geometry","volume":"28 1","pages":""},"PeriodicalIF":0.9000,"publicationDate":"2025-02-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Mathematical Physics, Analysis and Geometry","FirstCategoryId":"100","ListUrlMain":"https://link.springer.com/article/10.1007/s11040-025-09499-y","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}
引用次数: 0

Abstract

We study the umbilicity of constant mean curvature (CMC) complete hypersurfaces immersed in an Einstein manifold satisfying appropriate curvature constraints. In this setting, we obtain new characterization results for totally umbilical hypersurfaces via suitable maximum principles which deal with the notions of convergence to zero at infinity and polynomial volume growth. Afterwards, we establish optimal estimates for the first eigenvalue of the stability operator of CMC compact hypersurfaces in such an Einstein manifold. In particular, we derive a nonexistence result concerning strongly stable CMC hypersurfaces.

查看原文
分享 分享
微信好友 朋友圈 QQ好友 复制链接
本刊更多论文
求助全文
约1分钟内获得全文 去求助
来源期刊
Mathematical Physics, Analysis and Geometry
Mathematical Physics, Analysis and Geometry 数学-物理:数学物理
CiteScore
2.10
自引率
0.00%
发文量
26
审稿时长
>12 weeks
期刊介绍: MPAG is a peer-reviewed journal organized in sections. Each section is editorially independent and provides a high forum for research articles in the respective areas. The entire editorial board commits itself to combine the requirements of an accurate and fast refereeing process. The section on Probability and Statistical Physics focuses on probabilistic models and spatial stochastic processes arising in statistical physics. Examples include: interacting particle systems, non-equilibrium statistical mechanics, integrable probability, random graphs and percolation, critical phenomena and conformal theories. Applications of probability theory and statistical physics to other areas of mathematics, such as analysis (stochastic pde''s), random geometry, combinatorial aspects are also addressed. The section on Quantum Theory publishes research papers on developments in geometry, probability and analysis that are relevant to quantum theory. Topics that are covered in this section include: classical and algebraic quantum field theories, deformation and geometric quantisation, index theory, Lie algebras and Hopf algebras, non-commutative geometry, spectral theory for quantum systems, disordered quantum systems (Anderson localization, quantum diffusion), many-body quantum physics with applications to condensed matter theory, partial differential equations emerging from quantum theory, quantum lattice systems, topological phases of matter, equilibrium and non-equilibrium quantum statistical mechanics, multiscale analysis, rigorous renormalisation group.
期刊最新文献
Recurrence Relations for the Generalized Laguerre and Charlier Orthogonal Polynomials and Discrete Painlevé Equations on the \(D_{6}^{(1)}\) Sakai Surface Propagation of Chaos and Residual Dependence in Gibbs Measures on Finite Sets Matrix Solutions of the Cubic Szegő Equation on the Real Line A Novel Discrete Integrable System Related to Hyper-Elliptic Curves of Genus Two Umbilicity and the First Stability Eigenvalue of a Subclass of CMC Hypersurfaces Immersed in Certain Einstein Manifolds
×
引用
GB/T 7714-2015
复制
MLA
复制
APA
复制
导出至
BibTeX EndNote RefMan NoteFirst NoteExpress
×
×
提示
您的信息不完整,为了账户安全,请先补充。
现在去补充
×
提示
您因"违规操作"
具体请查看互助需知
我知道了
×
提示
现在去查看 取消
×
提示
确定
0
微信
客服QQ
Book学术公众号 扫码关注我们
反馈
×
意见反馈
请填写您的意见或建议
请填写您的手机或邮箱
已复制链接
已复制链接
快去分享给好友吧!
我知道了
×
扫码分享
扫码分享
Book学术官方微信
Book学术文献互助
Book学术文献互助群
群 号:481959085
Book学术
文献互助 智能选刊 最新文献 互助须知 联系我们:info@booksci.cn
Book学术提供免费学术资源搜索服务,方便国内外学者检索中英文文献。致力于提供最便捷和优质的服务体验。
Copyright © 2023 Book学术 All rights reserved.
ghs 京公网安备 11010802042870号 京ICP备2023020795号-1