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Isoperimetric control of thespectrum of a compact hypersurface

Colbois, Bruno ; El Soufi, Ahmad ; Girouard, Alexandre

In: Journal für die reine und angewandte Mathematik (Crelles Journal), 2013, vol. 2013, no. 683, p. 49-65

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    Title
    • Isoperimetric control of thespectrum of a compact hypersurface
    Author
    • Colbois, Bruno. Institut de Mathématiques, Université de Neuchâtel, Rue Emile-Argand 11, Case postale 158, 2009 Neuchâtel, Switzerland
    • El Soufi, Ahmad. Laboratoire de Mathématiques et Physique Théorique, UMR-CNRS 6083,Université Frano̧is Rabelais de Tours, Parc de Grandmont, 37200 Tours, France
    • Girouard, Alexandre. Institut de Mathématiques, Université de Neuchâtel, Rue Emile-Argand 11, Case postale 158, 2009 Neuchâtel, Switzerland
    Document Type
    • Postprint
    Language
    • English
    Published in
    • Journal für die reine und angewandte Mathematik (Crelles Journal), 2013, vol. 2013, no. 683, p. 49-65. Walter de Gruyter GmbH
    Other Version
    Classification
    • Health
    OAI-PMH Identifier
    • oai:doc.rero.ch:304527
    Summary
    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