Abstract
In this article, the growth theorems for some subclasses of biholomorphic mappings are obtained using the method of parametric representation. As the application, some well-known results can be got when special functions are taken on the unit disk in the complex plane.
Highlights
In geometric theory of one complex variable, the following growth theorem for biholomorphic functions was well known
Pointed out the above theorem for normalized biholomorphic mappings would not hold in several complex variables
Xiaofei Zhang completed his PhD degree in Pure Mathematics. The focus of his researches is in the geometric function theory of several complex variables
Summary
In geometric theory of one complex variable, the following growth theorem for biholomorphic functions was well known. Pointed out the above theorem for normalized biholomorphic mappings would not hold in several complex variables. He suggested to study the star-like mappings and convex mappings as appropriate topics for generalization. Untill 1991, Barnard, Fitzgerald, and Gong (1991) firstly established the growth and 1-theorems for normalized biholomorphic star-like mappings on the unit ball. Xiaofei Zhang completed his PhD degree in Pure Mathematics. The focus of his researches is in the geometric function theory of several complex variables. He is a lecturer of Pingdingshan University
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