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

被引：22

作者：

Pacard, Frank ^{[1
]}

Sicbaldi, Pieralberto ^{[1
]}

机构：

[1] Univ Paris Est, UFR Sci & Technol, F-94010 Creteil, France

来源：

ANNALES DE L INSTITUT FOURIER | 2009年 / 59卷 / 02期

关键词：

Extremal domain; Laplace-Beltrami operator; first eigenvalue; scalar curvature; geodesic sphere; CURVATURE;

D O I：

10.5802/aif.2438

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

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.

引用

页码：515 / 542

页数：28

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