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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Normality criteria for families of holomorphic
mappings of several complex variables into $P^N(C)$


Author: Zhen-han Tu
Journal: Proc. Amer. Math. Soc. 127 (1999), 1039-1049
MSC (1991): Primary 32A17, 32H25, 32H30; Secondary 30D35, 30D45
MathSciNet review: 1469438
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Abstract | References | Similar Articles | Additional Information

Abstract: By applying the heuristic principle in several complex variables obtained by Aladro and Krantz, we shall prove some normality criteria for families of holomorphic mappings of several complex variables into $P^N(C)$, the complex N-dimensional projective space, related to Green's and Nochka's Picard type theorems. The equivalence of normality to being uniformly Montel at a point will be obtained. Some examples will be given to complement our theory in this paper.


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Additional Information

Zhen-han Tu
Affiliation: Department of Mathematics, The University of Hong Kong, Pokfulam Road, Hong Kong; Department of Mathematics, Huazhong University of Science and Technology, Wuhan, Hubei 430074, People’s Republic of China
Email: H96920096@submaths.hku.hk

DOI: http://dx.doi.org/10.1090/S0002-9939-99-04610-9
PII: S 0002-9939(99)04610-9
Keywords: Complex projective spaces, holomorphic mappings, hyperplanes in general position, normality criteria and Picard type theorems
Received by editor(s): February 3, 1997
Received by editor(s) in revised form: July 14, 1997
Communicated by: Steven R. Bell
Article copyright: © Copyright 1999 American Mathematical Society