EXTREMAL DOMAINS FOR THE FIRST EIGENVALUE OF THE LAPLACE-BELTRAMI OPERATOR

We prove the existence of extremal domains with small prescribed volume for the first eigenvalue of Laplace-Beltrami operator in some Riemannian 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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Bibliographic Details
Published in:	Annales de l'Institut Fourier Vol. 59; no. 2; pp. 515 - 542
Main Authors:	PACARD, Frank, SICBALDI, Pieralberto
Format:	Journal Article
Language:	English
Published:	Grenoble Association des annales de l'institut Fourier 2009 Association des Annales de l'Institut Fourier
Subjects:	Analysis of PDEs Differential Geometry Exact sciences and technology General mathematics General, history and biography Geometry Global analysis, analysis on manifolds Mathematical analysis Mathematics Partial differential equations Sciences and techniques of general use Topology. Manifolds and cell complexes. Global analysis and analysis on manifolds Domains Laplace operator Sphere Volume Geodesic Eigenvalue Mathematics Critical point
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Description
Summary:	We prove the existence of extremal domains with small prescribed volume for the first eigenvalue of Laplace-Beltrami operator in some Riemannian manifold. These domains are close to geodesic spheres of small radius centered at a nondegenerate critical point of the scalar curvature.
ISSN:	0373-0956 1777-5310
DOI:	10.5802/aif.2438