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On Strongly Normal Functions

Published online by Cambridge University Press:  20 November 2018

Huaihui Chen  and
Paul M. Gauthier
Huaihui Chen
Affiliation:
Department of Mathematics, Nanjing Normal University, NanjingJiangsu 210024, RR. CHINA, [email protected]
Paul M. Gauthier
Affiliation:
Département de Mathématiques et de Statistique, Université de Montréal, MontréalQuébec H3C 3J7, CANADA, [email protected]
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Abstract

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Loosely speaking, a function (meromorphic or harmonic) from the hyperbolic disk of the complex plane to the Riemann sphere is normal if its dilatation is bounded. We call a function strongly normal if its dilatation vanishes at the boundary. A sequential property of this class of functions is proved. Certain integral conditions, known to be sufficient for normality, are shown to be in fact sufficient for strong normality.

Keywords

30D45Normal functionsautomorphic functions
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 39 , Issue 4 , 01 December 1996 , pp. 408 - 419
Copyright
Copyright © Canadian Mathematical Society 1996

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