%0 Journal Article
%T Extremal domains for the first eigenvalue in a general compact Riemannian manifold
%+ EA2151 Laboratoire de Mathématiques d'Avignon (LMA)
%+ Institut de Mathématiques de Marseille (I2M)
%A Delay, Erwann
%A Sicbaldi, Pieralberto
%< avec comité de lecture
%@ 1078-0947
%J Discrete and Continuous Dynamical Systems - Series A
%I American Institute of Mathematical Sciences
%V 35
%N 12
%P 5799-5825
%8 2015
%D 2015
%R 10.3934/dcds.2015.35.5799
%Z Mathematics [math]/Differential Geometry [math.DG]
%Z Mathematics [math]/Analysis of PDEs [math.AP]Journal articles
%X We prove the existence of extremal domains with small prescribed volume for the first eigenvalue of the Laplace-Beltrami operator in any compact Riemannian manifold. This result generalizes a results of F. Pacard and the second author where the existence of a nondegenerate critical point of the scalar curvature of the Riemannian manifold was required.
%G English
%2 https://hal.science/hal-01266512/document
%2 https://hal.science/hal-01266512/file/delay_sicbaldi1.pdf
%L hal-01266512
%U https://hal.science/hal-01266512
%~ UNIV-AVIGNON
%~ CNRS
%~ UNIV-AMU
%~ EC-MARSEILLE
%~ INSMI
%~ I2M
%~ I2M-2014-
%~ TDS-MACS
%~ LMA-UAPV