Eigenvalue pinching on convex domains in space forms

Aubry, Erwann; Bertrand, Jérôme; Colbois, Bruno

doi:10.1090/S0002-9947-08-04775-2

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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