2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/72161Lewis 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.35 pages, 1 figureAnalysis of PDEstext