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A Generalization of the Schwarz Lemma to Normal Selfaps of Complex Spaces

Part of: Holomorphic functions of several complex variables

Published online by Cambridge University Press:  09 April 2009

James E. Joseph  and
Myung H. Kwack
Myung H. Kwack
Affiliation:
Department of Mathematics Howard UniversityWashington, DC 20059USA e-mail: [email protected]
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Abstract

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We establish generalizations for normal selfmaps of complex spaces of the Schwarz lemma and of recent results on convergence of iterates of holomorphic selfmaps of taut spaces.

Keywords

Normalhyperbolictautly imbeddedfixed point

MSC classification

Secondary: 32A10: Holomorphic functions 32A17: Special families of functions
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 68 , Issue 1 , February 2000 , pp. 10 - 18
Copyright
Copyright © Australian Mathematical Society 2000

References

[1]Abate, M., Iteration therory of holomorphic maps on taut maniflods (Mediterrancean Press, Rende, Cosenza 1989).Google Scholar
[2]Hayman, W. K., ‘Uniformly normal families’, in: Lectures on functions of a complex variable (ed. Kaplan, ) (Univ. of Mich. Press, 1955) pp. 199–212.Google Scholar
[3]Hervé, M., Several complex variables, local theory (Oxford Univ. Press, London, 1963).Google Scholar
[4]Joseph, J. E. and Kwack, M. H., ‘Some classical theorems and families of normal maps in several complex variables’, Complex Variables 29 (1966), 343–378.Google Scholar
[5]Joseph, J. E., ‘Extension and convergence theorems for families of normal maps in serveral complex variables’, Proc. Amer. Math. Soc. 125 (1997), 1675–1684.CrossRefGoogle Scholar
[6]Kaup, W., ‘Reelle Transformationsgruppen und invariante Metriken auf komplexen Räumen’, Invent. Math. 3 (1967), 43–70.CrossRefGoogle Scholar
[7]Kobayashi, S., Complex hyperbolic spaces (Springer, New York, 1998).CrossRefGoogle Scholar
[8]Wu, H., ‘Normal families of holomorphic mappings’, Acta Math. 119 (1967), 193–233.CrossRefGoogle Scholar