拟共形映射的边界性态

本文利用曲线族的模数为工具,获得下述结果定理设D是扩充复数平面上的单连通区域,∞∈D,0 ∈ D, D/{0}≠φ并且D在点0是局部n-连通的,设S是发自原点的n-星散线(n条等角分布而不必等长的直线段),设W=f(z)是D到Ω=/S上的K-Q.C使得f(z)=0并且在∞满足就范条件

BOUNDARY BEHAVIOR OF QUASICONFORMAL

In this paper, to use modulus path famiLies as a tool, We obtain the following result THEOREM, Let D be a simpLy connected domain in with ∞∈D, 0∈D and {o}≠φ,which is Locally n-connected at 0, n≥1. S is a straight n-star at 0, Let W=f(z) is a K-Q.C. from D onto Ω=S, such that lim f(z)=0, and having the normalizations for every r>0, the D ∪B(r) has exactly n simply connected components D;(r) and O ∈D_i(r), 1≤j≤n. Let M_j(r)=sup |f(z)|. Then This result extended D. Aharonov and U. Srebro'S similar result in 1983 from the conformal mapping to K-Q.C.. mapping