Intended for mathematicians and algebraic analysts, this book provides a thorough introduction to the geometric and algebraic relationships between real hypersurfaces and complex analytical varieties. It covers a wide range of information, from basic facts about holomorphic functions of several complex variables, to deep results such as subelliptic estimates for the muNeumann problem of 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. It shows the reader how to decide wheter a real hypersurface contains complex varieties, how closely such varieties can contact the hypersurface and why it is important. The book concludes with two sets of problems: routine problems; and difficult problems (many of which are unsolved). Several concrete examples are included, such as for the local parametization theorem, the jump phenomena for the 1-type of a point on a hypersurface, and Kohn's method for computing ideal type. Principle prerequisites for using this book include a thorough understanding of advanced calculus and standard knowledge of complex analysis in one variable.
By:
John P. D'Angelo Series edited by:
StevenG. Krantz Imprint: CRC Press Inc Country of Publication: United States Volume: 8 Dimensions:
Height: 234mm,
Width: 156mm,
Spine: 18mm
Weight: 544g ISBN:9780849382727 ISBN 10: 0849382726 Series:Studies in Advanced Mathematics Pages: 288 Publication Date:06 January 1993 Audience:
College/higher education
,
Professional and scholarly
,
Professional & Vocational
,
A / AS level
,
Further / Higher Education
Format:Hardback Publisher's Status: Active
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.