拟圆周的一个几何特征

A Geometric Characterization of Quasicircles

利用几何知识给出了扩充复平面中的一条Jordan曲线是拟圆周的一个充要条件.

The following result is proved:if Γ is a Jordan curve of R^2,∞∈Γ,then Γ is a quasicircle if and only if there is a k,1≤k<+∞,such that,given any finite four points onΓ ,there exists a k-quasiconformal mapping h of R^2 onto itself with h(∞)=∞,h(Γ)=Γ and h(z_j)=w_j,for j=1,2.