TWO GEOMETRIC CHARACTERISTICS OF QUASICIRCLES  

作　　者：ChuYuming 

机构地区：[1]Dept.ofMath.,HuzhouNormalCollege,Huzhou313000,China

出　　处：《Applied Mathematics(A Journal of Chinese Universities)》2004年第2期155-159,共5页高校应用数学学报（英文版）（B辑）

基　　金：Supported by the National Natural Science Foundation of China( 1 0 2 71 0 4 3) and the Natural ScienceFoundation of Zhejiang province ( M1 0 30 87)

摘　　要：In this paper,the following two results are obtained:(1) If Γ is a Jordan curve of 2,∞∈Γ,then Γ is a quasicircle if and only if there exists a constant k,1≤k<+∞,such that for any four points z 1,z 2,w 1,w 2∈Γ,there exists a k-quasiconformal mapping h of 2 with h(∞)=∞,h(Γ)=Γ and h(z j)=w j(j=1,2).(2)If Γ is a Jordan curve of 2, then Γ is a quasicircle if and only if Γ is a bounded circular distortion curve.In this paper,the following two results are obtained:(1) If Γ is a Jordan curve of 2,∞∈Γ,then Γ is a quasicircle if and only if there exists a constant k,1≤k<+∞,such that for any four points z 1,z 2,w 1,w 2∈Γ,there exists a k-quasiconformal mapping h of 2 with h(∞)=∞,h(Γ)=Γ and h(z j)=w j(j=1,2).(2)If Γ is a Jordan curve of 2, then Γ is a quasicircle if and only if Γ is a bounded circular distortion curve.

关 键 词：quasiconformal mapping quasicircle bounded circular distortion curve. 

分 类 号：O18[理学—数学]