Ebook: Convex and Starlike Mappings in Several Complex Variables

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. It 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.
Audience: This volume will be of interest to research mathematicians whose work involves several complex variables and one complex variable.

---

---

Content:
Front Matter....Pages i-xiii
Introduction....Pages 1-17
Criteria for starlikeness for holomorphic mappings....Pages 18-43
Criteria for convexity for holomorphic mappings....Pages 44-77
The growth theorem for holomorphic starlike mappings....Pages 78-94
The growth theorem for holomorphic convex mappings....Pages 95-107
The distortion theorem for the linear-invariant family....Pages 108-136
The distortion theorem for holomorphic convex and starlike mappings....Pages 137-169
The geometrical properties for holomorphic convex mappings on the unit ball....Pages 170-188
Back Matter....Pages 189-209

---

Content:
Front Matter....Pages i-xiii
Introduction....Pages 1-17
Criteria for starlikeness for holomorphic mappings....Pages 18-43
Criteria for convexity for holomorphic mappings....Pages 44-77
The growth theorem for holomorphic starlike mappings....Pages 78-94
The growth theorem for holomorphic convex mappings....Pages 95-107
The distortion theorem for the linear-invariant family....Pages 108-136
The distortion theorem for holomorphic convex and starlike mappings....Pages 137-169
The geometrical properties for holomorphic convex mappings on the unit ball....Pages 170-188
Back Matter....Pages 189-209
....