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Transactions of the American Mathematical Society

Published by the American Mathematical Society since 1900, Transactions of the American Mathematical Society is devoted to longer research articles in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.48 .

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Eigenvalue pinching on convex domains in space forms
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by Erwann Aubry, Jérôme Bertrand and Bruno Colbois PDF
Trans. Amer. Math. Soc. 361 (2009), 1-18 Request permission

Abstract:

In this paper, we show that the convex domains of $\mathbb {H}^n$ which are almost extremal for the Faber-Krahn or the Payne-Polya-Weinberger inequalities are close to geodesic balls. Our proof is also valid in other space forms and allows us to recover known results in $\mathbb {R}^n$ and $\mathbb {S}^n$.
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Additional Information
  • Erwann Aubry
  • Affiliation: Laboratoire J.-A. Dieudonné, Université de Nice Sophia-Antipolis, UMR6621 (UNSA-CNRS), Parc Valrose, F-06108 Nice Cedex, France
  • Email: eaubry@math.unice.fr
  • Jérôme Bertrand
  • Affiliation: Institut de Mathématiques, Université de Toulouse of CNRS, UMR 5219, 118, route de Narbonne, F-31062 Toulouse, Cedex 4, France
  • Bruno Colbois
  • Affiliation: Institut de mathématiques, Université de Neuchâtel, Rue Émile Argand, 11, Case postale 158, CH-2009 Neuchâtel, Switzerland
  • MR Author ID: 50460
  • Email: bruno.colbois@unine.ch
  • Received by editor(s): April 26, 2006
  • Published electronically: August 19, 2008
  • Additional Notes: The first author was partially supported by FNRS Swiss Grant N. 20-101469.
  • © Copyright 2008 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 361 (2009), 1-18
  • MSC (2000): Primary 35P15, 35P05
  • DOI: https://doi.org/10.1090/S0002-9947-08-04775-2
  • MathSciNet review: 2439395