Stability of Lewis and Vogel’s result | Zendy

David Preiss | Zendy; Tatiana Toro | Zendy

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Stability of Lewis and Vogel’s result

Author(s) -

David Preiss,

Tatiana Toro

Publication year - 2007

Publication title -

revista matemática iberoamericana

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 1.569

H-Index - 52

eISSN - 2235-0616

pISSN - 0213-2230

DOI - 10.4171/rmi/485

Subject(s) - ball (mathematics) , bounded function , mathematics , measure (data warehouse) , poisson kernel , euclidean geometry , mathematical analysis , domain (mathematical analysis) , constant (computer programming) , poisson distribution , boundary (topology) , kernel (algebra) , euclidean space , pure mathematics , geometry , computer science , statistics , database , programming language

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.

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