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

Published online by Cambridge University Press:  09 April 2009

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.

Type
Research Article
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. 199212.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), 343378.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), 16751684.CrossRefGoogle Scholar
[6]Kaup, W., ‘Reelle Transformationsgruppen und invariante Metriken auf komplexen Räumen’, Invent. Math. 3 (1967), 4370.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), 193233.CrossRefGoogle Scholar