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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

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

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Equivalence of the classical theorems of Schottky, Landau, Picard and hyperbolicity
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by Kyong T. Hahn PDF
Proc. Amer. Math. Soc. 89 (1983), 628-632 Request permission

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
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Additional Information
  • © Copyright 1983 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 89 (1983), 628-632
  • MSC: Primary 30F10; Secondary 30C99, 32H15
  • DOI: https://doi.org/10.1090/S0002-9939-1983-0718986-4
  • MathSciNet review: 718986