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Transactions of the American Mathematical Society

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Eigenvalue pinching on convex domains in space forms

Authors: Erwann Aubry, Jérôme Bertrand and Bruno Colbois
Journal: Trans. Amer. Math. Soc. 361 (2009), 1-18
MSC (2000): Primary 35P15, 35P05
Published electronically: August 19, 2008
MathSciNet review: 2439395
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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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Erwann Aubry
Affiliation: Laboratoire J.-A. Dieudonné, Université de Nice Sophia-Antipolis, UMR6621 (UNSA-CNRS), Parc Valrose, F-06108 Nice Cedex, France

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

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.
Article copyright: © Copyright 2008 American Mathematical Society

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