An inequality à la Szegő-Weinberger for the Laplacian on convex sets
arXiv:1407.7422
Abstract
In this paper we prove a sharp inequality of Szegő-Weinberger type for the first nontrivial eigenvalue of the Laplacian with Neumann boundary conditions. This applies to convex sets with given diameter. Some variants, extensions and limit cases are investigated as well.