Extremal domains for the first eigenvalue of the Laplace-Beltrami operator
type: Item
instance of: scholarly article
title: Extremal domains for the first eigenvalue of the Laplace-Beltrami operator
zbMATH Open document ID: 1166.53029
author: Frank Pacard
author: Pieralberto Sicbaldi
publication date: 2009-04-29T00:00:00Z
full work available at URL: http://www.numdam.org/item
full work available at URL: https://eudml.org/doc/10402
review text: The main result of this paper is a proof for the existence of extremal domains with small prescribed volume for the first eigenvalue of the Laplace-Beltrami operator for certain Riemannian metrics. The domains are close to geodesic spheres of small radius centered at a nondegenerate critical point of the scalar curvature.
reviewed by: Radu Miron
Mathematics Subject Classification ID: 53C21
Mathematics Subject Classification ID: 58J50
zbMATH DE Number: 5548999
zbMATH Keywords: extremal domain
zbMATH Keywords: Laplace-Beltrami operator
zbMATH Keywords: first eigenvalue
zbMATH Keywords: scalar curvature
zbMATH Keywords: geodesic sphere
MaRDI profile type: Publication
OpenAlex ID: W2237975890
cites work: Sharp local isoperimetric inequalities involving the scalar curvature
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cites work: Q5817700
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cites work: Q4838145
cites work: Q4277833
cites work: Foliation by constant mean curvature spheres
cites work: Eigenvalue variations for the Neumann problem
DOI: 10.5802/AIF.2438
published in: Annales de l’institut Fourier
description: scientific article; zbMATH DE number 5548999