多复变量的K-拟共形映射  

On the Bloch Condtaut for K-Quasiconformal Mappings in Several Complex Variables

作　　者：Gamaliel J.Y. 陈怀惠[1] 

机构地区：[1]南京师范大学数学系,南京210097

出　　处：《数学学报（中文版）》2003年第2期317-320,共4页Acta Mathematica Sinica：Chinese Series

基　　金：国家自然科学基金资助项目;江苏省自然科学基金资助项目

摘　　要：本文研究Cn里的单位球B到Cn里的K-拟共形全纯映射.证明的最后结果是:若f是B到Cn里的K-拟共形全纯映射,满足det(f'(0))=1,则f(B)包含一个半径至少是(CnK)1-n∫01(1+t)N-1/(1-t)2exp{-(n+1)t/1-t}dt的单叶球,其中Cn>1是只依赖于n的常数,当n→∞时,Cn→(10)^(1/2).This paper study the Bloch constant for K-quasiconformal holomorphic mappings of the unit ball B of Cn. The final result we prove is: If f is a K-quasiconformal holomorphic mappings of the unit ball B of Cn such that det (f'(0)) = 1, then f(B)contains a schlicht ball of radius at least (CnK)1-n f01(1+t)n-1/(1-t)2 exp {-(n+1)t/1-t}dt where Cn > 1 is a constant depending on n only, and Cn→ 10 as n→∞.

关 键 词：K-拟共形全纯映射 BLOCH常数 全纯函数族 

分 类 号：O174.56[理学—数学]