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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Published in:arXiv.org 2021-08
Main Authors: Du, Feng, Mao, Jing, Qiao-Ling, Wang, Chang-Yu, Xia
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Language:English
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Domains
Eigenvalues
Euclidean geometry
Euclidean space
Hyperspaces
Manifolds
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description 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.
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subjects Domains
Eigenvalues
Euclidean geometry
Euclidean space
Hyperspaces
Manifolds
title Isoperimetric Bounds for Eigenvalues of the Wentzell-Laplace, the Laplacian and a biharmonic Steklov Problem
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