On the Julia directions of the value distribution of holomorphic curves in Pⁿ(C)

Abstract

The generalized Picard theorem [4] asserts that any non-constant holomorphic map f of C into Pⁿ(C) misses at most 2n hyperplanes in Pⁿ(C) in general position. In this paper we shall prove that for a transcendental holomorphic map f of C into Pⁿ(C) with an asymptotic value in Pⁿ(C), there exists a ray J(θ)={z=re√{−1}θ : 0<r<+∞} such that f, in any open sector with vertex z=0 containing the ray J(θ), misses at most 2n hyperplanes in Pⁿ(C) in general position.