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.
Publié le : 2007-04-14
Classification:
harmonic measure,
Fatou type theorems,
Poisson kernel,
Reifenberg flat,
28A75,
31A20,
35R35
@article{1180728884,
author = {Preiss, David and Toro, Tatiana},
title = {Stability of Lewis and Vogel's result},
journal = {Rev. Mat. Iberoamericana},
volume = {23},
number = {1},
year = {2007},
pages = { 17-55},
language = {en},
url = {http://dml.mathdoc.fr/item/1180728884}
}
Preiss, David; Toro, Tatiana. Stability of Lewis and Vogel's result. Rev. Mat. Iberoamericana, Tome 23 (2007) no. 1, pp. 17-55. http://gdmltest.u-ga.fr/item/1180728884/