Isoperimetric bounds for Wentzel-Laplace eigenvalues on Riemannian manifolds

Abstract

In this paper, we investigate eigenvalues of the Wentzel-Laplace operator on a bounded domain in some Riemannian manifold. We prove asymptotically optimal estimates, according to the Weyl's law through bounds that are given in terms of the isoperimetric ratio of the domain. Our results show that the isoperimetric ratio allows to control the entire spectrum of the Wentzel-Laplace operator in various ambient spaces.