# Stability of Lewis and Vogel's result

Research paper by D Preiss, T. Toro

Indexed on: 11 Aug '04Published on: 11 Aug '04Published in: Mathematics - Analysis of PDEs

#### 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.