Isoperimetric control of the spectrum of a compact hypersurface

Details Isoperimetric control of the spectrum of a compact hypersurface Isoperimetric control of the spectrum of a compact hypersurface

2010-07-06

arxiv.org/abs/1007.0826v2

Mathematics

Metric Geometry

To appear in Journal f\"ur die reine und angewandte Mathematik (Crelle's Journal)

Scientific paper

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.

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