DISTORTION THEOREMS FOR BLOCH MAPPINGS ON THE UNIT POLYDISC D^n  

作　　者：王建飞 刘太顺 唐笑敏 

机构地区：[1]College of Mathematics Physics and Information Engineering,Zhejiang Normal University [2]Department of Mathematics,Huzhou Teachers College

出　　处：《Acta Mathematica Scientia》2010年第5期1661-1668,共8页数学物理学报（B辑英文版）

基　　金：partly supported by the National Natural Science Foundation of China(10826083,10971063);NSF of Zhejiang Province (D7080080, Y606197,Y6090694);Scientific Research Fund of Zhejiang Provincial Education Department (Y200805520)

摘　　要：In this article, we establish distortion theorems for some various subfamilies of Bloch mappings defined in the unit polydisc Dn with critical points, which extend the results of Liu and Minda to higher dimensions. We obtain lower bounds of ｜ det（f＇（z））｜and Rdet（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.In this article, we establish distortion theorems for some various subfamilies of Bloch mappings defined in the unit polydisc Dn with critical points, which extend the results of Liu and Minda to higher dimensions. We obtain lower bounds of ｜ det（f＇（z））｜and Rdet（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.

关 键 词：Bloch constant Bloch mapping critical point holomorphic mapping 

分 类 号：O174.52[理学—数学]