Counterexamples Concerning Quasiconformal Extensions of Strongly Starlike Functions  

作　　者：Yu Liang SHEN 

机构地区：[1]Department of Mathematics, Suzhou University, Suzhou 215006, P. R. China

出　　处：《Acta Mathematica Sinica,English Series》2007年第10期1859-1868,共10页数学学报（英文版）

基　　金：This research was supported by NNSF of China(Grant No.10231040);NCET(06-0504)

摘　　要：M. Fait, J. Krzyz and J. Zygmunt proved that a strongly starlike function of order α on the unit disk can be extended to a k-quasiconformal mapping with k ≤ sin（απ/2） on the whole complex plane C which fixes the point at infinity. An open question is whether such a function can be extended to a k-quasiconformal mapping with k 〈α to the whole plane C. In this paper we will give a negative approach to the question.M. Fait, J. Krzyz and J. Zygmunt proved that a strongly starlike function of order α on the unit disk can be extended to a k-quasiconformal mapping with k ≤ sin（απ/2） on the whole complex plane C which fixes the point at infinity. An open question is whether such a function can be extended to a k-quasiconformal mapping with k 〈α to the whole plane C. In this paper we will give a negative approach to the question.

关 键 词：strongly starlike function quasiconformal extension Schwarzian derivative Teichmiiller mapping 

分 类 号：O18[理学—数学]