Isoperimetric Bounds for Eigenvalues of the Wentzell-Laplace, the Laplacian and a biharmonic Steklov Problem

In this paper, we prove some isoperimetric bounds for lower order eigenvalues of the Wentzell-Laplace operator on bounded domains of a Euclidean space or a Hadamard manifold, of the Laplacian on closed hypersurfaces of a Euclidean space or a Hadamard manifold, and of a biharmonic Steklov problem on...

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Bibliographic Details
Published in:arXiv.org 2021-08
Main Authors: Du, Feng, Mao, Jing, Qiao-Ling, Wang, Chang-Yu, Xia
Format: Article
Language:English
Subjects:
Domains
Eigenvalues
Euclidean geometry
Euclidean space
Hyperspaces
Manifolds
Online Access:Get full text
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Summary:In this paper, we prove some isoperimetric bounds for lower order eigenvalues of the Wentzell-Laplace operator on bounded domains of a Euclidean space or a Hadamard manifold, of the Laplacian on closed hypersurfaces of a Euclidean space or a Hadamard manifold, and of a biharmonic Steklov problem on bounded domains of a Euclidean space. Especially, interesting rigidity results can be obtained if sharp bounds were achieved.
ISSN:2331-8422