TWO GEOMETRIC CHARACTERISTICS OF QUASICIRCLES

摘要

In this paper, the following two results are obtained: (1) If Γ is a Jordan curve of R~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 R~2 with h(∞) = ∞, h(Γ) = Γ and A(z_j) =w_j(j=1, 2). (2)If Γ is a Jordan curve of R~2, then Γ is a quasicircle if and only if Γ is a bounded circular distortion curve.