Eigenvalue pinching on convex domains in space forms

Details Eigenvalue pinching on convex domains in space forms Eigenvalue pinching on convex domains in space forms

2006-04-26

arxiv.org/abs/math/0604576v1

Mathematics

Spectral Theory

submitted

Scientific paper

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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