Transactions of the American Mathematical Society

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Non-integrated defect relation for meromorphic maps of complete Kähler manifolds into $ \mathbb{P}^n(\mathbb{C})$ intersecting hypersurfaces


Authors: Min Ru and Suraizou Sogome
Journal: Trans. Amer. Math. Soc. 364 (2012), 1145-1162
MSC (2010): Primary 32H30; Secondary 53A10
Published electronically: October 24, 2011
MathSciNet review: 2869171
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Abstract: In this paper, we establish a non-integrated defect relation for a meromorphic map of a complete Kähler manifold whose universal covering is biholomorphic to a ball in $ \mathbb{C}^m$ into $ \mathbb{P}^n(\mathbb{C})$ intersecting hypersurfaces in general position, as well as an application to the Gauss map of a closed regular submanifold of $ \mathbb{C}^m$. The result provides a complement to the recent result of Ru (2004) on a defect relation for meromorphic mappings from $ \mathbb{C}^m$ into $ \mathbb{P}^n(\mathbb{C})$ intersecting hypersurfaces in general position.


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Additional Information

Min Ru
Affiliation: Department of Mathematics, University of Houston, Houston, Texas 77204
Email: minru@math.uh.edu

Suraizou Sogome
Affiliation: Department of Mathematics, University of Houston, Houston, Texas 77204
Email: ssogome@math.uh.edu

DOI: http://dx.doi.org/10.1090/S0002-9947-2011-05512-1
Keywords: Meromorphic mappings, Gauss map of minimal surfaces, defect relation, Nevanlinna theory
Received by editor(s): January 26, 2010
Published electronically: October 24, 2011
Additional Notes: The first author was supported in part by NSA under grant number H98230-09-1-0004 and H98230-11-0201
Article copyright: © Copyright 2011 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.