Acta mathematica scientia, Series B >
A DEGENERACY THEOREM FOR MEROMORPHIC MAPPINGS WITH TRUNCATED MULTIPLICITIES
Received date: 2009-07-02
Online published: 2011-03-20
Supported by
This project is supported by the National Natural Science Foundation of China (10871145, 10901120) and Doctoral Program Foundation of the Ministry of Education of China (20090072110053)
In this article, we prove a degeneracy theorem for three linearly non-degenerate meromorphic mappings from Cn into PN(C), sharing 2N+2 hyperplanes in general position, counted with multiplicities truncated by 2.
YAN Qi-Ming , CHEN Zhi-Hua . A DEGENERACY THEOREM FOR MEROMORPHIC MAPPINGS WITH TRUNCATED MULTIPLICITIES[J]. Acta mathematica scientia, Series B, 2011 , 31(2) : 549 -560 . DOI: 10.1016/S0252-9602(11)60255-5
[1] Nevanlinna R. Einige eidentigkeitssätze in der theorie der meromorphen funktionen. Acta Math, 1926, 48: 367--391
[2] Cartan H. Sur les syst\`{e}mes de fonctions holomorphes àvariétés linèaires lacunaires et leurs applications. Ann Sci Ècole Norm Sup, 1928, 45: 255--346
[3] Nevanlinna R. Le théorèmes de Picard-Borel et la thèorie des fonctions mèromorphes. Paris: Gauthier-Villars, 1929
[4] Cartan H. Un nouveau théorèmes d'unicité relatif aux fonctions méromorphes. C R Acad Sci Paris, 1929, 188: 301--303
[5] Steinmetz N. A uniqueness theorem for three meromorphic functions. Annales Acad Sci Fenn, 1988, 13: 93--110
[6] Fujimoto H. Uniqueness problem with truncated multiplicities in value distribution theory. Nagoya Math J, 1998, 152: 131--152
[7] Fujimoto H. The uniqueness problem of meromorphic maps into the complex projective spaces. Nagoya Math J, 1975, 58: 1--23
[8] Fujimoto H. A uniqueness theorem for algebraically non-degenerate meromorphic maps into PN (C). Nagoya Math J, 1976, 64: 117--147
[9] Fujimoto H. Remarks on the uniqueness problem of meromorphic maps into PN(C), III. Nagoya Math J, 1979, 75: 71--85
[10] Smiley L. Geometric conditions for unicity of holomorphic curves. Contemp Math, 1983, 25: 149--154
[11] Ji S. Uniqueness problem without multiplicities in value distribution theory. Pacific J Math, 1988, 135: 323--348
[12] Thai D D, Quang S D. Uniqueness problem with truncated multiplicities of meromorphic mappings in several complex variables.
Internat J Math, 2006, 17(10): 1223--1257
[13] Dethloff G, Tan T V. Uniqueness theorems for meromorphic mappings with few hyperplanes. Bull Sci Math, 2009, 133: 501--514
[14] Tan T V, Truong V V. Three meromorphic mappings sharing some common hyperplanes. J Math Anal Appl, 2008, 348: 562--570
[15] Chen Z, Yan Q. Uniqueness theorem of meromorphic mappings into PN(C) sharing 2N+3 hyperplanes regardless of multiplicities. Internat J Math, 2009, 20(6): 717--726
[16] Ru M. Nevanlinna theory and its relation to Diophantine approximation. Singapore: World Science Pub, 2001
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