Convex and Starlike Mappings in Several Complex Variables
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内容提要：
This book deals with the theory of convex and starlike biholomorphic mappings in several complex variables. The underlying theme is the extension to several complex variables of geometric aspects of the classical theory of univalent functions. This is the first book which systematically studies this topic. This book gathers together, and presents in a unified manner, the current state of affairs for convex and starlike biholomorphic mappings in several complex variables. The majority of the results presented are due to the author, his co-workers and his students. .
This volume will be of interest to research mathematicians whose work involves several complex variables and one complex variable. ... 目录：
Introduction §0.1 Introduction. §0.2 Counterexamples Chapter I Criteria for starlikeness for holomorphic mappings §1.1 Introduction §1.2 The criterion for starlikeness for holomorphic mappings on the bounded starlike circular domains §1.3 The criterion for starlikeness for holomorphic mappings on r-domains Chapter II Criteria for convexity for holomorphic mappings §2.1 Introduction §2.2 Criterion for convexity for holomorphic mappings on the unit ball §2.3 Decomposition theorem of holomorphic convex mappings §2.4 The expansion of biholomorphic convex mappings on Bp Chapter III The growth theorem for holomorphic starlike mappings §3.1 Introduction §3.2 The growth theorem for biholomorphic starlike mappings on the unit ball §3.3 The growth theorem for biholomorphic starlike mappings on Bp and classical domains §3.4 The growth theorem for biholomorphic starlike mappings on the bounded starlike circular domains Chapter IV The growth theorem for holomorphicconvex mappings §4.1 Introduction.. 前言：
This interesting book deals with the theory of convex and starlike biholomorphic mappings in several complex variables. The underlying theme is the extension to several complex variables of geometric aspects of the classical theory of univalent functions. Because the author's introduction provides an excellent overview of the content of the book, I will not duplicate the effort here. Rather, I will place the book into historical context. .
The theory of univalent functions long has been an important part of the study of holomorphic function..
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