JournalsrmiVol. 23, No. 1pp. 17–55

Stability of Lewis and Vogel’s result

  • David Preiss

    University of Warwick, Coventry, United Kingdom
  • Tatiana Toro

    Seattle University, USA
Stability of Lewis and Vogel’s result cover
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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 this article

David Preiss, Tatiana Toro, Stability of Lewis and Vogel’s result. Rev. Mat. Iberoam. 23 (2007), no. 1, pp. 17–55

DOI 10.4171/RMI/485