  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.
