Several Complex Variables and the Geometry of Real Hypersurfaces covers a wide range of information from basic facts about holomorphic functions of several complex variables through deep results such as subelliptic estimates for the ?-Neumann problem on pseudoconvex domains with a real analytic boundary. The book focuses on describing the geometry of a real hypersurface in a complex vector space by understanding its relationship with ambient complex analytic varieties. You will learn how to decide whether a real hypersurface contains complex varieties, how closely such varieties can contact the hypersurface, and why it's important. The book concludes with two sets of problems: routine problems and difficult problems (many of which are unsolved).
Principal prerequisites for using this book include a thorough understanding of advanced calculus and standard knowledge of complex analysis in one variable. Several Complex Variables and the Geometry of Real Hypersurfaces will be a useful text for advanced graduate students and professionals working in complex analysis.
Table of Contents
Holomorphic Functions and Mappings. Holomorphic Mappings and Local Algebra. Geometry of Real Hypersurfaces. Points of Finite Type. Proper Mappings between Balls. Geometry of the ?-Neumann Problem. Analysis on Finite Type Domains. Bibliography. Exercises. Index of Notation. Index.
John D'Angelo University of Illinois, USA.