Extremal domains for the first eigenvalue of the laplace-beltrami operator

Frank Pacard; Pieralberto Sicbaldi

doi:10.5802/aif.2438

Extremal domains for the first eigenvalue of the laplace-beltrami operator

Frank Pacard, Pieralberto Sicbaldi

Université de PARIS XII

Research output: Contribution to journal › Article › peer-review

Abstract

We prove the existence of extremal domains with small prescribed volume for the first eigenvalue of Laplace-Beltrami operator in some Rie- mannian manifold. These domains are close to geodesic spheres of small radius centered at a nondegenerate critical point of the scalar curvature.

Original language	English
Pages (from-to)	515-542
Number of pages	28
Journal	Annales de l'Institut Fourier
Volume	59
Issue number	2
DOIs	https://doi.org/10.5802/aif.2438
Publication status	Published - 1 Jan 2009
Externally published	Yes

Keywords

Extremal domain
First eigenvalue
Geodesic sphere
Laplace-beltrami operator
Scalar curvature

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10.5802/aif.2438

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title = "Extremal domains for the first eigenvalue of the laplace-beltrami operator",

abstract = "We prove the existence of extremal domains with small prescribed volume for the first eigenvalue of Laplace-Beltrami operator in some Rie- mannian manifold. These domains are close to geodesic spheres of small radius centered at a nondegenerate critical point of the scalar curvature.",

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author = "Frank Pacard and Pieralberto Sicbaldi",

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AU - Sicbaldi, Pieralberto

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N2 - We prove the existence of extremal domains with small prescribed volume for the first eigenvalue of Laplace-Beltrami operator in some Rie- mannian manifold. These domains are close to geodesic spheres of small radius centered at a nondegenerate critical point of the scalar curvature.

AB - We prove the existence of extremal domains with small prescribed volume for the first eigenvalue of Laplace-Beltrami operator in some Rie- mannian manifold. These domains are close to geodesic spheres of small radius centered at a nondegenerate critical point of the scalar curvature.

KW - Extremal domain

KW - First eigenvalue

KW - Geodesic sphere

KW - Laplace-beltrami operator

KW - Scalar curvature

U2 - 10.5802/aif.2438

DO - 10.5802/aif.2438

M3 - Article

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SN - 0373-0956

VL - 59

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JO - Annales de l'Institut Fourier

JF - Annales de l'Institut Fourier

IS - 2

ER -

Extremal domains for the first eigenvalue of the laplace-beltrami operator

Abstract

Keywords

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