Several Complex Variables and the Geometry of Real Hypersurfaces

This book provides an in-depth exploration of real hypersurfaces in complex vector spaces, emphasizing their connections with complex analytic varieties.

In Several Complex Variables and the Geometry of Real Hypersurfaces, the author delves into the intricate geometry of real hypersurfaces situated within complex vector spaces. The text emphasizes the essential connections between these hypersurfaces and the surrounding complex analytic varieties. By exploring this relationship, readers gain insights into how real hypersurfaces can contain complex varieties and the significance of their interactions.

The book offers a comprehensive overview, starting with fundamental concepts related to holomorphic functions of multiple complex variables. It progresses into more advanced topics, including subelliptic estimates for the ?-Neumann problem on pseudoconvex domains with real analytic boundaries. This progression ensures that readers not only grasp the basics but also engage with profound results that are critical in the field of complex analysis.

To enhance understanding, the author includes two sets of problems at the conclusion of the book: routine exercises and more challenging unsolved problems. These problems serve to solidify the reader's knowledge and encourage further exploration in the subject. A solid foundation in advanced calculus and complex analysis in one variable is recommended for those looking to fully engage with the material presented in Several Complex Variables and the Geometry of Real Hypersurfaces.