Eigenvalue pinching on convex domains in space forms
Spectral Theory
2007-05-23 v1 Differential Geometry
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.
Keywords
Cite
@article{arxiv.math/0604576,
title = {Eigenvalue pinching on convex domains in space forms},
author = {E. Aubry and J. Bertrand and B. Colbois},
journal= {arXiv preprint arXiv:math/0604576},
year = {2007}
}
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