Isoperimetric control of the spectrum of a compact hypersurface

Abstract

Upper bounds for the eigenvalues of the Laplace-Beltrami operator on a hypersurface bounding a domain in some ambient Riemannian manifold are given in terms of the isoperimetric ratio of the domain. These results are applied to the extrinsic geometry of isometric embeddings.

arXiv commentTo appear in Journal für die reine und angewandte Mathematik (Crelle's Journal)