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A symmetry theorem revisited

Authors: John Lewis and Andrew Vogel
Journal: Proc. Amer. Math. Soc. 130 (2002), 443-451
MSC (1991): Primary 31B05, 31B20
Published electronically: June 6, 2001
MathSciNet review: 1862124
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We show that if harmonic measure and Hausdorff measure are equal on the boundary of certain domains in Euclidean $n$-space, then these domains are necessarily balls.

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Additional Information

John Lewis
Affiliation: Department of Mathematics, University of Kentucky, Lexington, Kentucky 40506-0027

Andrew Vogel
Affiliation: Department of Mathematics, Syracuse University, Syracuse, New York 13244

Keywords: Harmonic measure, Hausdorff measure, quasiconformal, Green's function, Dirichlet problem
Received by editor(s): June 20, 2000
Published electronically: June 6, 2001
Additional Notes: The first author was supported in part by an NSF grant
Communicated by: Juha M. Heinonen
Article copyright: © Copyright 2001 American Mathematical Society

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