{"title":"Isoperimetric inequalities for Neumann eigenvalues on bounded domains in rank-1 symmetric spaces","authors":"Yifeng Meng, Kui Wang","doi":"10.1007/s00526-024-02726-4","DOIUrl":null,"url":null,"abstract":"<p>In this paper, we prove sharp isoperimetric inequalities for lower order eigenvalues of Neumann Laplacian on bounded domains in both compact and noncompact rank-1 symmetric spaces. Our results generalize the work of Wang and Xia for bounded domains in the hyperbolic space (Xia and Wang in Math Ann 385(1–2):863–879, 2023), and Szegö–Weinberger inequalities in rank-1 symmetric spaces obtained by Aithal and Santhanam (Trans Am Math Soc 348(10):3955–3965, 1996).</p>","PeriodicalId":9478,"journal":{"name":"Calculus of Variations and Partial Differential Equations","volume":"39 1","pages":""},"PeriodicalIF":2.1000,"publicationDate":"2024-04-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Calculus of Variations and Partial Differential Equations","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1007/s00526-024-02726-4","RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 0
Abstract
In this paper, we prove sharp isoperimetric inequalities for lower order eigenvalues of Neumann Laplacian on bounded domains in both compact and noncompact rank-1 symmetric spaces. Our results generalize the work of Wang and Xia for bounded domains in the hyperbolic space (Xia and Wang in Math Ann 385(1–2):863–879, 2023), and Szegö–Weinberger inequalities in rank-1 symmetric spaces obtained by Aithal and Santhanam (Trans Am Math Soc 348(10):3955–3965, 1996).
在本文中，我们证明了紧凑和非紧凑秩-1对称空间有界域上诺伊曼拉普拉奇低阶特征值的尖锐等周不等式。我们的结果概括了王和夏针对双曲空间有界域的研究成果（夏和王在《数学年刊》385(1-2):863-879, 2023），以及艾瑟尔和桑塔纳姆在秩-1对称空间中获得的斯泽格-温伯格不等式（Trans Am Math Soc 348(10):3955-3965, 1996）。
期刊介绍：
Calculus of variations and partial differential equations are classical, very active, closely related areas of mathematics, with important ramifications in differential geometry and mathematical physics. In the last four decades this subject has enjoyed a flourishing development worldwide, which is still continuing and extending to broader perspectives.
This journal will attract and collect many of the important top-quality contributions to this field of research, and stress the interactions between analysts, geometers, and physicists. The field of Calculus of Variations and Partial Differential Equations is extensive; nonetheless, the journal will be open to all interesting new developments. Topics to be covered include:
- Minimization problems for variational integrals, existence and regularity theory for minimizers and critical points, geometric measure theory
- Variational methods for partial differential equations, optimal mass transportation, linear and nonlinear eigenvalue problems
- Variational problems in differential and complex geometry
- Variational methods in global analysis and topology
- Dynamical systems, symplectic geometry, periodic solutions of Hamiltonian systems
- Variational methods in mathematical physics, nonlinear elasticity, asymptotic variational problems, homogenization, capillarity phenomena, free boundary problems and phase transitions
- Monge-Ampère equations and other fully nonlinear partial differential equations related to problems in differential geometry, complex geometry, and physics.
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