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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

Convex sets and subharmonicity of the distance function


Author: M. J. Parker
Journal: Proc. Amer. Math. Soc. 103 (1988), 503-506
MSC: Primary 31B05; Secondary 52A20
MathSciNet review: 943074
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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.


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DOI: https://doi.org/10.1090/S0002-9939-1988-0943074-6
Keywords: Convex set, subharmonic function
Article copyright: © Copyright 1988 American Mathematical Society