基于任意拟圆的对数导数意义下区域的单叶性内径

The Inner Radius of Univalence in the Sense of Pre-Schwarzian Derivative Based on any Quasidisk

研究了对数导数意义下区域的单叶性内径。以任意拟圆为基础,给出了区域对数导数单叶性内径下界的两个公式。此外,根据逼近区域的特征得到了区域的对数导数单叶性内径的另一个下界公式,并由此估计出正多边形的单叶性内径的上界。

In this paper, the inner radius of univalency of hyperbolic domains by pre - Schwarzian derivative is studied. Based on any quasidisk, two general formulas for the lower bound on inner radius of univalence in the sense of pre - Schwarzian derivative were established. In addition, by means of the properties of regions approaching to given domain, it gets another lower bound on inner radius of univalence, and estimates the upper bound on inner radius of univalenee for regular polygon by our results.