A note on uniqueness problem for meromorphic mappings with 2N+3 hyperplanes  

作　　者：ZhiHua Chen QiMing Yan 

机构地区：[1]Tongji Univ, Dept Math, Shanghai 200092, Peoples R China

出　　处：《Science China Mathematics》2010年第10期2657-2663,共7页中国科学：数学（英文版）

基　　金：supported by National Natural Science Foundation of China (Grant Nos.10871145,10901120);Doctoral Program Foundation of the Ministry of Education of China (Grant No.20090072110053)

摘　　要：In this paper,a uniqueness theorem for meromorphic mappings partially sharing 2N+3 hyperplanes is proved.For a meromorphic mapping f and a hyperplane H,set E(H,f) = {z|ν(f,H)(z) 】 0}.Let f and g be two linearly non-degenerate meromorphic mappings and {Hj}j2=N1+ 3be 2N + 3 hyperplanes in general position such that dim f-1(Hi) ∩ f-1(Hj) n-2 for i = j.Assume that E(Hj,f) E(Hj,g) for each j with 1 j 2N +3 and f = g on j2=N1+ 3f-1(Hj).If liminfr→+∞ 2j=N1+ 3N(1f,Hj)(r) j2=N1+ 3N(1g,Hj)(r) 】 NN+1,then f ≡ g.In this paper,a uniqueness theorem for meromorphic mappings partially sharing 2N+3 hyperplanes is proved.For a meromorphic mapping f and a hyperplane H,set E(H,f) = {z|ν(f,H)(z) > 0}.Let f and g be two linearly non-degenerate meromorphic mappings and {Hj}j2=N1+ 3be 2N + 3 hyperplanes in general position such that dim f-1(Hi) ∩ f-1(Hj) n-2 for i = j.Assume that E(Hj,f) E(Hj,g) for each j with 1 j 2N +3 and f = g on j2=N1+ 3f-1(Hj).If liminfr→+∞ 2j=N1+ 3N(1f,Hj)(r) j2=N1+ 3N(1g,Hj)(r) > NN+1,then f ≡ g.

关 键 词：value distribution theory UNIQUENESS theorem MEROMORPHIC MAPPINGS 

分 类 号：N[自然科学总论]