A unicity theorem for meromorphic maps of a complete Kähler manifold into sharing hypersurfaces

Authors:
Min Ru and Suraizou Sogome

Journal:
Proc. Amer. Math. Soc. **141** (2013), 4229-4239

MSC (2010):
Primary 32H30; Secondary 53A10

DOI:
https://doi.org/10.1090/S0002-9939-2013-11718-1

Published electronically:
August 1, 2013

MathSciNet review:
3105866

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Abstract | References | Similar Articles | Additional Information

Abstract: In this paper, we give a unicity theorem for meromorphic maps of an dimensional complete Kähler manifold , whose universal covering is a ball in , into , sharing the hypersurfaces in general position in , where the maps satisfy a certain growth condition.

**1.**T. T. H. An and H. T. Phuong, An explicit estimate on multiplicity truncation in the Second Main Theorem for holomorphic curves encountering hypersurfaces in general position in projective space,*Houston J. Math.***35**(2009), 775-786. MR**2534280 (2010i:30048)****2.**H. Fujimoto, Uniqueness problem with truncated multiplicities in value distribution theory,*Nagoya Math. J.***152**(1998), 131-152. MR**1659377 (99m:32029)****3.**H. Fujimoto, Non-integrated defect relation for meromorphic maps of complete Kähler manifolds into ,*Japan. J. Math.***11**(1985), no. 2, 233-264. MR**884636 (88m:32049)****4.**H. Fujimoto, Value distribution theory of the Gauss maps of complete minimal surfaces in ,*J. Math. Soc. Japan***35**(1983), 663-681. MR**714468 (85c:53011)****5.**H. Fujimoto, A unicity theorem for meromorphic maps of a complete Kähler manifold into ,*Tôhoku Math. J.***38**(1986), 327-341. MR**843816 (87j:32078)****6.**W. K. Hayman, Meromorphic functions,*Oxford Mathematical Monographs,*Clarendon Press, Oxford, 1964. MR**0164038 (29:1337)****7.**L. Karp, Subharmonic functions on real and complex manifolds,*Math. Z.***179**(1982), 535-554. MR**652859 (84d:53042)****8.**R. Nevanlinna, Einige Eindeutigkeitassätze in der theorie der meromorphen Funktionen,*Acta. Math.***48**(1926), 367-391. MR**1555233****9.**M. Ru, A defect relation for holomorphic curves intersecting hypersurfaces,*Amer. J. Math.***126**(2004), 215-226. MR**2033568 (2004k:32026)****10.**M. Ru, Holomorphic curves into algebraic varieties,*Ann. of Math. (2)***169**(2009), 255-267. MR**2480605 (2010d:32009)****11.**M. Ru and S. Sogome, Non-integrated defect relation for meromorphic maps of complete Kähler manifold intersecting hypersurfaces in ,*Trans. Amer. Math. Soc.***364**(2012), 1145-1162. MR**2869171****12.**M. Dulock and M. Ru, A uniqueness theorem for holomorphic curves encountering hypersurfaces in projective space,*Complex Variables and Elliptic Equations***53**(2008), 797-802. MR**2436255 (2009e:32019)****13.**W. Stoll, Introduction to value distribution theory of meromorphic maps,*Lecture Notes in Math.***950**(1982), 210-359. MR**672787 (84a:32041)****14.**S.-T. Yau, Some function-theoretic properties of complete Riemannian manifolds and their applications to geometry,*Indiana U. Math. J.***25**(1976), 659-670. MR**0417452 (54:5502)****15.**A. Vitter, The lemma of the logarithmic derivative in several variables,*Duke Math. J.***44**(1977), 89-104. MR**0432924 (55:5903)**

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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:
Suraizou.Sogome@lonestar.edu

DOI:
https://doi.org/10.1090/S0002-9939-2013-11718-1

Received by editor(s):
October 17, 2011

Received by editor(s) in revised form:
January 30, 2012

Published electronically:
August 1, 2013

Additional Notes:
The first author was supported in part by NSA H98230-11-1-0201

Communicated by:
Mei-Chi Shaw

Article copyright:
© Copyright 2013
American Mathematical Society

The copyright for this article reverts to public domain 28 years after publication.