Convex and Starlike Mappings in Several Complex Variables, Softcover reprint of the original 1st ed. 1998 Mathematics and Its Applications Series, Vol. 435

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.

I Criteria for starlikeness for holomorphic mappings.- II Criteria for convexity for holomorphic mappings.- III The growth theorem for holomorphic starlike mappings.- IV The growth theorem for holomorphic convex mappings.- V The distortion theorem for the linearinvariant family.- VI The distortion theorem for holomorphic convex and starlike mappings.- VII The geometrical properties for holomorphic convex mappings on the unit ball.- References.- List of symbols.