数学物理学报(英文版) ›› 2010, Vol. 30 ›› Issue (5): 1631-1639.doi: 10.1016/S0252-9602(10)60156-7

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ON THE EXISTENCE OF SINGULAR DIRECTIONS OF HOLOMORPHIC MAPS FROM THE UNIT DISK INTO Pn(C)

涂振汉, 张莎莎   

  1. School of Mathematics and Statistics, Wuhan University, Wuhan 430072, China  
  • 收稿日期:2008-08-30 修回日期:2009-02-24 出版日期:2010-09-20 发布日期:2010-09-20
  • 基金资助:

    The project supported in part by the National Natural Science Foundation of China (10971156).

ON THE EXISTENCE OF SINGULAR DIRECTIONS OF HOLOMORPHIC MAPS FROM THE UNIT DISK INTO Pn(C)

 TU Zhen-Han, ZHANG Sha-Sha   

  1. School of Mathematics and Statistics, Wuhan University, Wuhan 430072, China
  • Received:2008-08-30 Revised:2009-02-24 Online:2010-09-20 Published:2010-09-20
  • Supported by:

    The project supported in part by the National Natural Science Foundation of China (10971156).

摘要:

This article proves the existence of Julia directions of value distribution of holomorphic mapping f from the unit disk into the n-dimensional complex projective space Pn(C) under the assumption limits_{r\rightarrow 1^{-}} T(r, f)/ log 1/1-r= +∞ for hypersurfaces in general position. A heuristic principle concerning the existence of Julia directions of holomorphic mappings from the unit disk into Pn(C) is given also.

关键词: complex projective spaces, holomorphic mapping, Julia direction, Picards theorem, value distribution theory

Abstract:

This article proves the existence of Julia directions of value distribution of holomorphic mapping f from the unit disk into the n-dimensional complex projective space Pn(C) under the assumption limits_{r\rightarrow 1^{-}} T(r, f)/ log 1/1-r= +∞ for hypersurfaces in general position. A heuristic principle concerning the existence of Julia directions of holomorphic mappings from the unit disk into Pn(C) is given also.

Key words: complex projective spaces, holomorphic mapping, Julia direction, Picards theorem, value distribution theory

中图分类号: 

  • 32H25