Transactions of the American Mathematical Society

Author(s): Erwann Aubry; Jérôme Bertrand; Bruno Colbois
Journal: Trans. Amer. Math. Soc. 361 (2009), 1-18.
MSC (2000): Primary 35P15, 35P05
Posted: August 19, 2008
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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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Retrieve articles in Transactions of the American Mathematical Society with MSC (2000): 35P15, 35P05

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
Email: bruno.colbois@unine.ch

DOI: 10.1090/S0002-9947-08-04775-2
PII: S 0002-9947(08)04775-2
Received by editor(s): April 26, 2006
Posted: August 19, 2008
Additional Notes: The first author was partially supported by FNRS Swiss Grant N. 20-101469.
Copyright of article: Copyright 2008, American Mathematical Society

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