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Eigenvalue pinching on convex domains in space forms

Abstract : In this paper, we show that the convex domains of the hyperbolic space 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 Euclidean space and on the sphere.
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https://hal.archives-ouvertes.fr/hal-00338161
Contributor : Erwann Aubry <>
Submitted on : Tuesday, November 11, 2008 - 6:29:35 PM
Last modification on : Wednesday, June 9, 2021 - 10:00:07 AM

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Erwann Aubry, Jérôme Bertrand, Bruno Colbois. Eigenvalue pinching on convex domains in space forms. Transactions of the American Mathematical Society, American Mathematical Society, 2009, 361 (1), pp.1--18. ⟨hal-00338161⟩

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