Distortion theorems for Bloch mappings on the unit polydisc D n

Abstract

In this article, we establish distortion theorems for some various subfamilies of Bloch mappings defined in the unit polydisc D n with critical points, which extend the results of Liu and Minda to higher dimensions. We obtain lower bounds of |det ( f'( z))| and ℝ det ( f'( z)) for Bloch mapping f. As an application, some lower and upper bounds of Bloch constants for the subfamilies of holomorphic mappings are given.