Stability of Lewis and Vogel's result

Details Stability of Lewis and Vogel's result Stability of Lewis and Vogel's result

2004-08-11

arxiv.org/abs/math/0408145v1

Mathematics

Analysis of PDEs

35 pages, 1 figure

Scientific paper

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.

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