正则区域的对数导数单叶性内径
The Inner Radius of Univalence by Pre-Schwarzian Derivative of Regulated Domain

研究了单位圆到正则区域的共形映射的对数导数,讨论了对数导数范数的一些性质,得到了带凸角的正则区域在对数导数意义下的单叶性内径的一个下界估计,并推导出椭圆内部区域的对数导数意义下的单叶性内径为1.
Making use of integral representation of a conformal map from the unit disk onto a regulated domain,the pre-Schwarzian derivative of the conformal map is discussed.A new estimation of lower bound of the inner radius of univalence by pre-Schwarzian derivative of a regulated domain with convex corners is obtained