一致区域的定义及单叶性准则

THE DEFINITION FOR UNIFORM DOMAIN AND UNIVALENCE CRITERION

O.Martio, J.Sarvas及F. W . Gehring, B. G.Osgood分别给出了一致区域的定义。本文给出了一致区域的一个形式上非常简单的新定义,并且证明了它与上面两个定义的等价性。在这个定义的基础上,我们得出了一个函数的单叶性定理。最后,对穿孔圆盘的单叶性内径给出了一个估计。

In this paper, a new definition for uniform domain is given and the following theorem is proved. Let D is (α,β) -uniform domain in C 0<α≤β<∞. f is an analytic founction in D. and f,(z)≠0. if Thten f is uniualent in D. We also obtain a estimate for inner radius σ_3 of univalence on disk wih hole