Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

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

 

 

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
DOI: https://doi.org/10.1090/S0002-9939-1983-0718986-4
MathSciNet review: 718986
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

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?)


Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 30F10, 30C99, 32H15

Retrieve articles in all journals with MSC: 30F10, 30C99, 32H15


Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1983-0718986-4
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