Convex sets and subharmonicity of the distance function
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- by M. J. Parker PDF
- Proc. Amer. Math. Soc. 103 (1988), 503-506 Request permission
Abstract:
In this paper we show that in order for a proper closed subset $F$ of a plane domain $D$ to be convex it is necessary and sufficient that $\operatorname {dist}( \cdot ,F)$ be subharmonic in $D$. We also show that this result does not hold for higher dimensions.References
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Additional Information
- © Copyright 1988 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 103 (1988), 503-506
- MSC: Primary 31B05; Secondary 52A20
- DOI: https://doi.org/10.1090/S0002-9939-1988-0943074-6
- MathSciNet review: 943074