万有Teichmuller空间Pre-Schwarz导数模型及拟共形扩张  

Quasiconformal Extension Property and the Universal Teichmuller Space by Pre-Schwarzian Derivative

作　　者：康悦明[1] 程涛 陈纪修[4] 

机构地区：[1]上海对外贸易学院商务信息学院,上海201620 [2]中国科学院数学与系统科学研究院,北京100080 [3]江西师范大学数学与信息科学学院,南昌330027 [4]复旦大学数学科学学院,上海200433

出　　处：《数学年刊（A辑）》2008年第6期851-858,共8页Chinese Annals of Mathematics

基　　金：国家自然科学基金(No．10571028);上海高校选拔培养优秀青年教师科研专项基金资助的项目．

摘　　要：主要研究了一些对应于万有Teichmuller空间Pre-Schwarz导数模型中点的函数的拟共形扩张,得到了函数的拟共形扩张的复伸张与之Pre-Schwarz导数范数的一些关系,最后,通过具体构造一类函数的拟共形扩张表达式,得到了角域的Pre-Schwarz导数单叶性内径下界估计的另一种证明方法。This paper investigates some quasiconformal extensions of the functions corresponding to the points in the universal Teichmuller space by Pre-Schwarzian derivative, and finds some connections between the complex dilatations of the quasiconformal extension functions and the norms of the Pre-Schwarzian derivatives. In the last section of the paper, the authors find another proof for the lower bound of the inner radius of univalency for angular domains by constructing an explicit quasiconformal extension of a class of holomorphic functions.

关 键 词：PRE-SCHWARZ导数 单叶性内径 万有Teichmuller空间 拟共形扩张 

分 类 号：O174.55[理学—数学]