拟共形映照的非爆破性  

The non-explosion of quasi-conformal mapping

作　　者：韩雪[1] 

机构地区：[1]华侨大学数学科学学院,福建泉州362021

出　　处：《贵州师范学院学报》2011年第6期11-13,共3页Journal of Guizhou Education University

基　　金：华侨大学科研基金资助项目(09HZR23)

摘　　要：R.M.Portor定义了K—拟共形映照在非欧度量下的双曲面积问题。若双曲面积有限的可测集合在某拟共形映照下的面积为无限的,则称此集合为爆破集,拟共形映照为爆破的。继【1】研究了单位圆上的径向映照的爆破性,并估计了其双曲面积偏差的基础上,进一步研究更一般的函数类,得到了它的非爆破的性质。另外,还研究了单位圆上的调和拟共形映照类,得到了它的非爆破性质。R.M.Protor defines the hyperbolic metric under K-quasi-conformal mapping.The set with finite hyperbolic area is said to be k-explodable and the quasi-conformal mapping is explodable if there exists a quasi-conformal mapping and its hyperbolic area is infinite,Based on the [1] study on the radial mapping defined in the unit disk,and the estimation of the hyperbolic area distortion,we study the more general function class and find the condition which makes them nonexplodable.Then the quasi-conformal harmonic mapping in the unit disk is studied and its non-explosion has been proved.

关 键 词：拟共形映照 单叶调和映照 双曲面积 爆破 

分 类 号：O174.55[理学—数学]