Eigenvalue pinching on convex domains in space forms

2006/04/26 by E. Aubry, Aubry, E., J. Bertrand +3
Mathematics · #Differential Geometry (math.DG) #FOS: Mathematics #Spectral Theory (math.SP) #math.DG #math.SP

paper · pdf · doi:10.48550/arxiv.math/0604576

submitted

arxiv created 2006/04/26 · arxiv updated 2009/12/01

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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