On the Julia directions of the value distribution of holomorphic curves in ${\rm P}^n({\bf C})$

Abstract

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