关于一致域一个特征的初等证明

An Elementary Proof of a Characteristic of the Uniform Domains

利用初等的方法和John圆技术证明了R2中的任一有限连通域D是一致域当且仅当D的每一边界分支均为拟圆周或一点.由此得出结论:平面一致域是拟圆的推广.

We prove that a finite connected domain D R^2 is a uniform domain if and only if each bounda ry component of D is a quasi - circle or a point by using the elementary computation and John disk tech nique, and conclude that the uniform domain in R^2 is the generalization of the quasidisk.