单叶p-调和映射

主要目的是介绍两个p-调和映射类HS_p和HC_p及其相应的子类HS_p^0和H_p^0,同时研究这些类中映射的性质.首先,讨论了HS_p^0和HC_p^0中映射的几何性质.证明了在HS_p^0和HC_p^0中的映射下,单位圆盘的像域分别是星形的和凸的.其次,确定了HS_p^0、H_p^0、HS_p∩T_p和HC_p∩T_p的极值点,其中T_p表示具有非负系数的p-调和映射类.最后,证明了HC_p中映射邻域的存在性.

The Roper-Suffridge extension operator and classes of biholomorphic mappings Dedicated to Professor Sheng GONG on the occasion of his 75th birthday

In this paper we give a survey about the Roper-Suffridge extension operator and the developments in the theory of univalent mappings in several variables to which it has led. We begin with the basic geometric properties (most of which now have a number of different proofs)and discuss relations with the theory of Loewner chains and generalizations and modifications of the operator, some of which are very recent.