关于Loewner微分方程

ON LOEWNER DIFFERENTIAL EQUATION

本文研究了单裂纹映照所生成的Loewner链,得到Loewner微分方程中的函数k(t)∈C^(1)[0,+∞)的一个充分条件。在这个条外下,Loewner微分方程可以连续延拓到边界。

In this paper,we study the Loewner chain produced by a single slit mapp-ing.A sufficient condition is obtained.Under this condition,the function k(t)in the Loewner equation is continuously differetiable on[0,∞),and the Loewnerequation can be continuously extended to the boundary |z|=1.