Extremal domains for the first eigenvalue of the Laplace-Beltrami operator

Frank Pacard (1) , Pieralberto Sicbaldi (1)

1 LAMA - Laboratoire d'Analyse et de Mathématiques Appliquées

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.

Domaines: Géométrie différentielle [math.DG]; Equations aux dérivées partielles [math.AP]

Frank Pacard, Pieralberto Sicbaldi. Extremal domains for the first eigenvalue of the Laplace-Beltrami operator. Annales de l'Institut Fourier, 2009, ⟨10.5802/aif.2438⟩. ⟨hal-01266405⟩