Existence and regularity of Faber Krahn minimizers in a Riemannian manifold

Jimmy Lamboley, Pieralberto Sicbaldi

In this paper, we study the minimization of ${\lambda }_1(\Omega )$, the first Dirichlet eigenvalue of the Laplace-Beltrami operator, within the class of open sets $\Omega$ of fixed volume in a Riem…