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April, 2007 Stability of Lewis and Vogel's result
David Preiss, Tatiana Toro
Rev. Mat. Iberoamericana 23(1): 17-55 (April, 2007).

Abstract

Lewis and Vogel proved that a bounded domain whose Poisson kernel is constant and whose surface measure to the boundary has at most Euclidean growth is a ball. In this paper we show that this result is stable under small perturbations. In particular a bounded domain whose Poisson kernel is smooth and close to a constant, and whose surface measure to the boundary has at most Euclidean growth is a smooth deformation of a ball.

Citation

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David Preiss. Tatiana Toro. "Stability of Lewis and Vogel's result." Rev. Mat. Iberoamericana 23 (1) 17 - 55, April, 2007.

Information

Published: April, 2007
First available in Project Euclid: 1 June 2007

zbMATH: 1122.31002
MathSciNet: MR2351125

Subjects:
Primary: 28A75, 31A20, 35R35

Rights: Copyright © 2007 Departamento de Matemáticas, Universidad Autónoma de Madrid

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Vol.23 • No. 1 • April, 2007
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