Several Complex Variables and the Geometry of Real Hypersurfaces
Author | : John P. D'Angelo |
Publisher | : CRC Press |
Total Pages | : 350 |
Release | : 1993-01-06 |
ISBN-10 | : 0849382726 |
ISBN-13 | : 9780849382727 |
Rating | : 4/5 (26 Downloads) |
Book excerpt: 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.