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

doi:10.1016/S0252-9602(10)60156-7

Abstract

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

CLC Number:

32H25

TU Zhen-Han, ZHANG Sha-Sha. ON THE EXISTENCE OF SINGULAR DIRECTIONS OF HOLOMORPHIC MAPS FROM THE UNIT DISK INTO Pⁿ(C)[J].Acta mathematica scientia,Series B, 2010, 30(5): 1631-1639.

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

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