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Proceedings of the American Mathematical Society

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Subharmonicity, the distance function, and $ a$-admissible sets


Author: Stephen J. Gardiner
Journal: Proc. Amer. Math. Soc. 112 (1991), 979-981
MSC: Primary 31B05
DOI: https://doi.org/10.1090/S0002-9939-1991-1065946-7
MathSciNet review: 1065946
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Abstract: Let $ \Omega $ be an open subset of $ {\mathbb{R}^n}$. The main result of this paper shows that a one-sided control on the curvature of $ \partial \Omega $ is equivalent to subharmonicity of a function related to $ \operatorname{dist}(X,\partial \Omega )$. An application is given.


References [Enhancements On Off] (What's this?)

  • [1] D. H. Armitage and Ü. Kuran, The convexity of a domain and the superharmonicity of the signed distance function, Proc. Amer. Math. Soc. 93 (1985), 598-600. MR 776186 (86k:31005)
  • [2] Ü. Kuran, On positive superharmonic functions in $ a$-admissible domains, J. London Math. Soc. (2) 29 (1984), 269-275. MR 744097 (85j:31005)
  • [3] M. J. Parker, Convex sets and subharmonicity of the distance function, Proc. Amer. Math. Soc. 103 (1988), 503-506. MR 943074 (89e:31005)

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DOI: https://doi.org/10.1090/S0002-9939-1991-1065946-7
Article copyright: © Copyright 1991 American Mathematical Society

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