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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.
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Contributor : Ahmad El Soufi <>
Submitted on : Friday, September 30, 2011 - 9:31:09 PM
Last modification on : Friday, February 19, 2021 - 4:10:02 PM
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Bruno Colbois, Ahmad El Soufi, Alexandre Girouard. Isoperimetric control of the spectrum of a compact hypersurface. Journal für die reine und angewandte Mathematik, Walter de Gruyter, 2013, 683, pp.49--65. ⟨10.1515/crelle-2012-0008⟩. ⟨hal-00497630v2⟩

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