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