New Examples of Extremal Domains for the First Eigenvalue of the Laplace–Beltrami Operator in a Riemannian Manifold with Boundary
Jimmy Lamboley, Pieralberto Sicbaldi · International Mathematics Research Notices · 2014
We build new examples of extremal domains with small prescribed volume for the first eigenvalue of the Laplace–Beltrami operator in some Riemannian manifolds with boundary. These domains are close to half-balls of small radius centered at a nondegenerate critical point of the mean curvature function of the boundary of the manifold, and their boundary intersects the boundary of the manifold orthogonally.