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- W2078194857 abstract "Let X be a simply connected and hyperbolic subregion of the complex plane C . A proper subregion Ω of X is called hyperbolically convex in X if for any two points A and B in Ω , the hyperbolic geodesic arc joining A and B in X is always contained in Ω . We establish a number of characterizations of hyperbolically convex regions Ω in X in terms of the relative hyperbolic density ρ Ω ( w ) of the hyperbolic metric of Ω to X , that is the ratio of the hyperbolic metric λ Ω ( w ) | d w | of Ω to the hyperbolic metric λ X ( w ) | d w | of X . Introduction of hyperbolic differential operators on X makes calculations much simpler and gives analogous results to some known characterizations for euclidean or spherical convex regions. The notion of hyperbolic concavity relative to X for real-valued functions on Ω is also given to describe some sufficient conditions for hyperbolic convexity." @default.
- W2078194857 created "2016-06-24" @default.
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- W2078194857 date "2005-09-01" @default.
- W2078194857 modified "2023-09-26" @default.
- W2078194857 title "Characterizations of hyperbolically convex regions" @default.
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- W2078194857 doi "https://doi.org/10.1016/j.jmaa.2004.12.008" @default.
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