Extremal domains for the first eigenvalue in a general Riemannian manifold

2013/02/18 by Delay, Erwann, Sicbaldi, Pieralberto
#Differential Geometry (math.DG) #FOS: Mathematics

paper · doi:10.48550/arxiv.1302.4221

Abstract

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.

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