The convexity of a domain and the superharmonicity of the signed distance function
Authors: D. H. Armitage and Ü. Kuran
Journal: Proc. Amer. Math. Soc. 93 (1985), 598-600
MSC: Primary 31B05; Secondary 52A20
MathSciNet review: 776186
Abstract: Let be a domain in with nonempty boundary and let be the signed distance function from , i.e. dist according as we are in or outside . We prove that, for any is superharmonic in if and only if is convex. When , this criterion requires the superharmonicity of in only.