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Revista Matemática Iberoamericana


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Volume 23, Issue 1, 2007, pp. 17–55
DOI: 10.4171/RMI/485

Published online: 2007-04-30

Stability of Lewis and Vogel’s result

David Preiss[1] and Tatiana Toro[2]

(1) University of Warwick, Coventry, United Kingdom
(2) Seattle University, USA

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.

Keywords: Harmonic measure, Poisson kernel, Reifenberg flat

Preiss David, Toro Tatiana: Stability of Lewis and Vogel’s result. Rev. Mat. Iberoam. 23 (2007), 17-55. doi: 10.4171/RMI/485