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CARLSON–GRIFFITHS THEORY FOR COMPLETE KÄHLER MANIFOLDS

Part of: Entire and meromorphic functions, and related topics Holomorphic mappings and correspondences

Published online by Cambridge University Press:  14 February 2022

Xianjing Dong Open the ORCID record for Xianjing Dong [Opens in a new window]
Xianjing Dong*
Affiliation:
School of Mathematics, China University of Mining and Technology, Xuzhou, 221116, P. R. China
*
xjdong@amss.ac.cn
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Abstract

We investigate Carlson–Griffiths’ equidistribution theory of meormorphic mappings from a complete Kähler manifold into a complex projective algebraic manifold. By using a technique of Brownian motions developed by Atsuji, we obtain a second main theorem in Nevanlinna theory provided that the source manifold is of nonpositive sectional curvature. In particular, a defect relation follows if some growth condition is imposed.

Keywords

Nevanlinna theoryvalue distributionsecond main theoremlogarithmic derivative lemmadefect relation

MSC classification

Primary: 30D35: Distribution of values, Nevanlinna theory
Secondary: 32H30: Value distribution theory in higher dimensions
Type
Research Article
Information
Journal of the Institute of Mathematics of Jussieu , Volume 22 , Issue 5 , September 2023 , pp. 2337 - 2365
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Copyright
© The Author(s), 2022. Published by Cambridge University Press

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