### Abstract

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.

Original language | English (US) |
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Pages (from-to) | 443-451 |

Number of pages | 9 |

Journal | Proceedings of the American Mathematical Society |

Volume | 130 |

Issue number | 2 |

DOIs | |

State | Published - Jan 1 2002 |

Externally published | Yes |

### Keywords

- Dirichlet problem
- Green's function
- Harmonic measure
- Hausdorff measure
- Quasiconformal

### ASJC Scopus subject areas

- Mathematics(all)
- Applied Mathematics

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## Cite this

Lewis, J., & Vogel, A. (2002). A symmetry theorem revisited.

*Proceedings of the American Mathematical Society*,*130*(2), 443-451. https://doi.org/10.1090/S0002-9939-01-06200-1