Inserted: 6 jun 2016
Last Updated: 6 jun 2016
Journal: International Mathematics Research Notices, IMRN
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.