Stability of Lewis and Vogel's result

D Preiss; T. Toro

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Stability of Lewis and Vogel's result

D Preiss·T. Toro

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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.

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D Preiss, T. Toro. 2004-08-11. Stability of Lewis and Vogel's result. https://arxiv.org/abs/math/0408145

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