Extremal domains for the first eigenvalue of the Laplace-Beltrami operator
The main result of this paper is a proof for the existence of extremal domains with small prescribed volume for the first eigenvalue of the Laplace-Beltrami operator for certain Riemannian metrics. The domains are close to geodesic spheres of small radius centered at a nondegenerate critical point of the scalar curvature.
scientific article; zbMATH DE number 5548999