%0 Journal Article
%T Extremal domains of big volume for the first eigenvalue of the Laplace-Beltrami operator in a compact manifold
%+ Institut de Mathématiques de Marseille (I2M)
%A Sicbaldi, Pieralberto
%< avec comité de lecture
%@ 0294-1449
%J Annales de l'Institut Henri Poincaré C, Analyse non linéaire
%I EMS
%V 31
%N 6
%P 1231-1265
%8 2014
%D 2014
%Z Mathematics [math]/Differential Geometry [math.DG]
%Z Mathematics [math]
%Z Mathematics [math]/Analysis of PDEs [math.AP]Journal articles
%X We prove the existence of extremal domains for the first eigenvalue of the Laplace-Beltrami operator in some compact Riemannian manifolds, with volume close to the volume of the manifold. If the first (positive) eigenfunction F of the Laplace-Beltrami operator over the manifold is a nonconstant function, these domains are close to the complement of geodesic balls of small radius whose center is close to the point where F attains its maximum. If F is a constant function and the dimension of the manifold is at least 4, these domains are close to the complement of geodesic balls of small radius whose center is close to a nondegenerate critical point of the scalar curvature function.
%G English
%2 https://hal.science/hal-00480303v2/document
%2 https://hal.science/hal-00480303v2/file/paper_sicbaldi_AnnIHP.pdf
%L hal-00480303
%U https://hal.science/hal-00480303
%~ CNRS
%~ UNIV-AMU
%~ EC-MARSEILLE
%~ I2M
%~ I2M-2014-
%~ TDS-MACS