Bloch Constant of Holomorphic Mappings on the Unit Ball of C^n  

作　　者：Jianfei WANG Taishun LIU 

机构地区：[1]Department of Mathematics, University of Science and Technology of China, Hefei 230026, China [2]Department of Mathematics, Huzhou Teachers College, Huzhou 313000, Zhejiang, China

出　　处：《Chinese Annals of Mathematics,Series B》2007年第6期677-684,共8页数学年刊（B辑英文版）

基　　金：Project supported by the National Natural Science Foundation of China(No.10571164);Specialized Research Fund for the Doctoral Program of Higher Education(No.20050358052);the Zhejiang Provincial Natural Science Foundation of China(No.Y606197).

摘　　要：In this paper, the authors establish distortion theorems for various subfamilies Hk（B） of holomorphic mappings defined in the unit ball in C^n with critical points, where k is any positive integer. In particular, the distortion theorem for locally biholomorphic mappings is obtained when k tends to -∞. These distortion theorems give lower bounds on [det f′（z）[ and Re det f′（z）. As an application of these distortion theorems, the authors give lower and upper bounds of Bloch constants for the subfamilies βk（M） of holomorphic mappings. Moreover, these distortion theorems are sharp. When B is the unit disk in C, these theorems reduce to the results of Liu and Minda. A new distortion result of Re det f′（z） for locally biholomorphic mappings is also obtained.

关 键 词：Bloch constant Holomorphic mappings Locally biholomorphic mappings Critical points 

分 类 号：O174.5[理学—数学]