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

2018/08/31 by Du, Feng, Mao, Jing, Wang, Qiao-Ling +1
#35P15 #53C40 #58C40 #Differential Geometry (math.DG) #FOS: Mathematics

paper · doi:10.48550/arxiv.1808.10578

Abstract

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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