On Locally Quasiconformal Mappings  

作　　者：Ze Min ZHOU 

机构地区：[1]Department of Mathematics,Renmin University of China

出　　处：《Acta Mathematica Sinica,English Series》2013年第8期1543-1554,共12页数学学报（英文版）

基　　金：Supported by National Natural Science Foundation of China (Grant No 10971030)

摘　　要：A homeomorphism w=f（z） of a domain D is called a locally quasiconformal mapping, if for each subdomain D＇ of D with ＇D, the restriction of f（z） on D＇ is a quasiconformal mapping. We give some conditions for a measurable function μ（z） on the unit disc to be the complex dilatation of a locally quasiconformal mapping f which can be homeomorphically extended to the closed unit disc.A homeomorphism w=f（z） of a domain D is called a locally quasiconformal mapping, if for each subdomain D＇ of D with ＇D, the restriction of f（z） on D＇ is a quasiconformal mapping. We give some conditions for a measurable function μ（z） on the unit disc to be the complex dilatation of a locally quasiconformal mapping f which can be homeomorphically extended to the closed unit disc.

关 键 词：HOMEOMORPHISM quasiconformal mapping locally quasiconformal mapping directional dilatation 

分 类 号：O174.55[理学—数学] O174.5[理学—基础数学]