Degeneracy theorems for holomorphic mappings from a complex disc with finite growth index

Abstract

In this paper, we prove degeneracy theorems for holomorphic mappings from a complex disc ∆(R) ⊂ C with finite growth index into P (C) sharing hyperplanes in general position. We further consider the case that intersecting points of the mappings and the hyperplanes with multiplicities more than a certain number do not need to be counted. These results generalize the previous degeneracy theorems for meromorphic mappings from C into P(C)