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

Résultats de recherche: Contribution à un journal › Article › Revue par des pairs

Résumé

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.

langue originale	Anglais
Pages (de - à)	515-542
Nombre de pages	28
journal	Annales de l'Institut Fourier
Volume	59
Numéro de publication	2
Les DOIs	https://doi.org/10.5802/aif.2438
état	Publié - 1 janv. 2009
Modification externe	Oui

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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.",

keywords = "Extremal domain, First eigenvalue, Geodesic sphere, Laplace-beltrami operator, Scalar curvature",

author = "Frank Pacard and Pieralberto Sicbaldi",

year = "2009",

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AU - Pacard, Frank

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

AN - SCOPUS:67149097669

SN - 0373-0956

VL - 59

SP - 515

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JO - Annales de l'Institut Fourier

JF - Annales de l'Institut Fourier

IS - 2

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

Résumé

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