Extremal domains of big volume for the first eigenvalue of the Laplace–Beltrami operator in a compact manifold

  • Pieralberto Sicbaldi

    Université d'Aix-Marseille, France

Abstract

We prove the existence of new extremal domains for the first eigenvalue of the Laplace–Beltrami operator in some compact Riemannian manifolds of dimension . The volume of such domains is close to the volume of the manifold. If the first eigenfunction of the Laplace–Beltrami operator over the manifold is a nonconstant function, these domains are close to the complement of geodesic balls centered at a nondegenerate critical point of . If is a constant function and , these domains are close to the complement of geodesic balls centered at a nondegenerate critical point of the scalar curvature.

Cite this article

Pieralberto Sicbaldi, Extremal domains of big volume for the first eigenvalue of the Laplace–Beltrami operator in a compact manifold. Ann. Inst. H. Poincaré Anal. Non Linéaire 31 (2014), no. 6, pp. 1231–1265

DOI 10.1016/J.ANIHPC.2013.09.001