A sharp estimate for Neumann eigenvalues of the Laplace–Beltrami operator for domains in a hemisphere-Reference-Cited by-同舟云学术

A sharp estimate for Neumann eigenvalues of the Laplace–Beltrami operator for domains in a hemisphere

Published:2019-03-28 Issue:03 Volume:22 Page:1950018
ISSN:0219-1997
Container-title:Communications in Contemporary Mathematics
language:en
Short-container-title:Commun. Contemp. Math.

Author:

Benguria Rafael D.¹,Brandolini Barbara²,Chiacchio Francesco²

Affiliation:

1. Instituto de Física, Facultad de Física, P. Universidad Católica de Chile, Casilla 306, Santiago 22, Chile

2. Dipartimento di Matematica e Applicazioni “R. Caccioppoli”, Università degli Studi di Napoli “Federico II”, Complesso Monte S. Angelo – Via Cintia, 80126 Napoli, Italy

Abstract

Here, we prove an isoperimetric inequality for the harmonic mean of the first [Formula: see text] non-trivial Neumann eigenvalues of the Laplace–Beltrami operator for domains contained in a hemisphere of [Formula: see text].

Funder

Fondecyt

Publisher

World Scientific Pub Co Pte Lt

Subject

Applied Mathematics,General Mathematics

Link

https://www.worldscientific.com/doi/pdf/10.1142/S0219199719500184

Reference15 articles.

1. Open Problems on Eigenvalues of the Laplacian

2. A Sharp Bound for the Ratio of the First Two Eigenvalues of Dirichlet Laplacians and Extensions

3. Universal Bounds for the Low Eigenvalues of Neumann Laplacians inNDimensions