Stability of Lewis and Vogel's result
Analysis of PDEs
2007-05-23 v1
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.
Cite
@article{arxiv.math/0408145,
title = {Stability of Lewis and Vogel's result},
author = {D Preiss and T. Toro},
journal= {arXiv preprint arXiv:math/0408145},
year = {2007}
}
Comments
35 pages, 1 figure