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Equivalence of the classical theorems of Schottky, Landau, Picard and hyperbolicity

Author: Kyong T. Hahn
Journal: Proc. Amer. Math. Soc. 89 (1983), 628-632
MSC: Primary 30F10; Secondary 30C99, 32H15
MathSciNet review: 718986
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Abstract: Modifying the classical theorems of Schottky and Landau, the author obtains the converses of these theorems. More precisely, the author defines the notions of Schottky, Landau and Picard properties and proves that a plane domain $ D$ satisfies any of these properties if and only if $ {\mathbf{C}}\backslash D$ contains at least two points. The method of proofs is completely elementary and uses only some basic properties of the Kobayashi metric.

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

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Keywords: Classical theorems of Schottky and Landau, Schottky-property, Landau-property, Picard-property, Kobayashi metric, hyperbolicity, Poincaré metric
Article copyright: © Copyright 1983 American Mathematical Society

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