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Journal für die reine und angewandte Mathematik

Managing Editor: Weissauer, Rainer

Ed. by Colding, Tobias / Huybrechts, Daniel / Hwang, Jun-Muk / Williamson, Geordie


IMPACT FACTOR 2017: 1.686

CiteScore 2017: 0.96

SCImago Journal Rank (SJR) 2017: 2.585
Source Normalized Impact per Paper (SNIP) 2017: 1.203

Mathematical Citation Quotient (MCQ) 2016: 1.28

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1435-5345
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Volume 2013, Issue 683

Issues

Isoperimetric control of the spectrum of a compact hypersurface

Bruno Colbois
  • Institut de Mathématiques, Université de Neuchâtel, Rue Emile-Argand 11, Case postale 158, 2009 Neuchâtel, Switzerland
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/ Ahmad El Soufi
  • Laboratoire de Mathématiques et Physique Théorique, UMR-CNRS 6083, Université Frano̧is Rabelais de Tours, Parc de Grandmont, 37200 Tours, France
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/ Alexandre Girouard
  • Institut de Mathématiques, Université de Neuchâtel, Rue Emile-Argand 11, Case postale 158, 2009 Neuchâtel, Switzerland
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Published Online: 2012-04-03 | DOI: https://doi.org/10.1515/crelle-2012-0008

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.

About the article

Received: 2010-09-25

Revised: 2011-11-16

Published Online: 2012-04-03

Published in Print: 2013-10-01


Citation Information: Journal für die reine und angewandte Mathematik (Crelles Journal), Volume 2013, Issue 683, Pages 49–65, ISSN (Online) 1435-5345, ISSN (Print) 0075-4102, DOI: https://doi.org/10.1515/crelle-2012-0008.

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