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Normal families of meromorphic mappings of several complex variables for moving hypersurfaces in a complex projective space

Part of: Holomorphic functions of several complex variables Holomorphic mappings and correspondences

Published online by Cambridge University Press:  11 January 2016

Gerd Dethloff ,
Do Duc Thai  and
Pham Nguyen Thu Trang
Gerd Dethloff
Affiliation:
Université Européenne de Bretagne, France, Université de Brest, Laboratoire de Mathématiques Bretagne Atlantique - UMR CNRS 6205, 29238 Brest Cedex 3, France, [email protected]
Do Duc Thai
Affiliation:
Department of Mathematics, Hanoi National University of Education, Hanoi, Vietnam, [email protected]
Pham Nguyen Thu Trang
Affiliation:
Department of Mathematics, Hanoi National University of Education, Hanoi, Vietnam, [email protected]
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Abstract

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The main aim of this article is to give sufficient conditions for a family of meromorphic mappings of a domain D in ℂn into ℙN(ℂ) to be meromorphically normal if they satisfy only some very weak conditions with respect to moving hypersurfaces in ℙN(ℂ), namely, that their intersections with these moving hypersurfaces, which moreover may depend on the meromorphic maps, are in some sense uniform. Our results generalize and complete previous results in this area, especially the works of Fujimoto, Tu, Tu-Li, Mai-Thai-Trang, and the recent work of Quang-Tan.

MSC classification

Secondary: 32A19: Normal families of functions, mappings 32H30: Value distribution theory in higher dimensions
Type
Research Article
Information
Nagoya Mathematical Journal , Volume 217 , March 2015 , pp. 23 - 59
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 2015

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