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

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.**Ta Thi Hoai An and Ha Tran 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), no. 3, 775–786. MR**2534280****2.**Hirotaka Fujimoto,*Uniqueness problem with truncated multiplicities in value distribution theory*, Nagoya Math. J.**152**(1998), 131–152. MR**1659377****3.**Hirotaka Fujimoto,*Nonintegrated defect relation for meromorphic maps of complete Kähler manifolds into 𝑃^{𝑁₁}(𝐶)×\cdots×𝑃^{𝑁_{𝑘}}(𝐶)*, Japan. J. Math. (N.S.)**11**(1985), no. 2, 233–264. MR**884636****4.**Hirotaka Fujimoto,*Value distribution of the Gauss maps of complete minimal surfaces in 𝑅^{𝑚}*, J. Math. Soc. Japan**35**(1983), no. 4, 663–681. MR**714468**, 10.2969/jmsj/03540663**5.**Hirotaka Fujimoto,*A unicity theorem for meromorphic maps of a complete Kähler manifold into 𝑃^{𝑁}(𝐶)*, Tohoku Math. J. (2)**38**(1986), no. 2, 327–341. MR**843816**, 10.2748/tmj/1178228497**6.**W. K. Hayman,*Meromorphic functions*, Oxford Mathematical Monographs, Clarendon Press, Oxford, 1964. MR**0164038****7.**Leon Karp,*Subharmonic functions on real and complex manifolds*, Math. Z.**179**(1982), no. 4, 535–554. MR**652859**, 10.1007/BF01215065**8.**Rolf Nevanlinna,*Einige Eindeutigkeitssätze in der Theorie der Meromorphen Funktionen*, Acta Math.**48**(1926), no. 3-4, 367–391 (German). MR**1555233**, 10.1007/BF02565342**9.**Min Ru,*A defect relation for holomorphic curves intersecting hypersurfaces*, Amer. J. Math.**126**(2004), no. 1, 215–226. MR**2033568****10.**Min Ru,*Holomorphic curves into algebraic varieties*, Ann. of Math. (2)**169**(2009), no. 1, 255–267. MR**2480605**, 10.4007/annals.2009.169.255**11.**Min Ru and Suraizou Sogome,*Non-integrated defect relation for meromorphic maps of complete Kähler manifolds into ℙⁿ(ℂ) intersecting hypersurfaces*, Trans. Amer. Math. Soc.**364**(2012), no. 3, 1145–1162. MR**2869171**, 10.1090/S0002-9947-2011-05512-1**12.**Matthew Dulock and Min Ru,*A uniqueness theorem for holomorphic curves sharing hypersurfaces*, Complex Var. Elliptic Equ.**53**(2008), no. 8, 797–802. MR**2436255**, 10.1080/17476930802127081**13.**Wilhelm Stoll,*Introduction to value distribution theory of meromorphic maps*, Complex analysis (Trieste, 1980) Lecture Notes in Math., vol. 950, Springer, Berlin-New York, 1982, pp. 210–359. MR**672787****14.**Shing Tung Yau,*Some function-theoretic properties of complete Riemannian manifold and their applications to geometry*, Indiana Univ. Math. J.**25**(1976), no. 7, 659–670. MR**0417452****15.**Al Vitter,*The lemma of the logarithmic derivative in several complex variables*, Duke Math. J.**44**(1977), no. 1, 89–104. MR**0432924**

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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.