Complex Analysis Several Complex Variables and Connections with PDE Theory and Geometry 1st Edition by Peter Ebenfelt, Norbert Hungerbuhler, Joseph J Kohn, Ngaiming Mok, Emil J Straube ISBN 3034600089 9783034600088

Complex Analysis Several Complex Variables and Connections with PDE Theory and Geometry 1st Edition by Peter Ebenfelt, Norbert Hungerbuhler, Joseph J. Kohn, Ngaiming Mok, Emil J. Straube – Ebook PDF Instant Download/Delivery: 3034600089, 9783034600088
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ISBN 10: 3034600089 
ISBN 13: 9783034600088
Author: Peter Ebenfelt, Norbert Hungerbuhler, Joseph J. Kohn, Ngaiming Mok, Emil J. Straube

This volume offers a deep and multifaceted exploration of the rich interplay between several complex variables (SCV), partial differential equations (PDEs), and differential geometry. Developed from a conference organized by the Swiss Mathematical Society in honor of Professor Linda Rothschild, a leading figure in the field, the book brings together contributions from some of the most respected mathematicians working in complex analysis and its geometric and analytic applications. Its purpose is not only to honor Rothschild’s mathematical legacy but also to highlight the dynamic developments in the field, particularly the ways in which SCV theory informs, and is informed by, methods from PDEs and differential geometry.

The book is both a tribute and a research compendium, offering expository surveys alongside original research articles. It is particularly notable for its coverage of topics such as the ∂̄-Neumann problem, CR (Cauchy-Riemann) geometry, Bergman kernel methods, and the structure of pseudoconvex domains—all of which are central to modern SCV theory and find critical applications in solving boundary value problems and understanding geometric structures in complex manifolds. Through its carefully curated chapters, the volume illustrates how techniques from SCV can be used to address significant questions in analysis and geometry, including the regularity of solutions to complex PDEs, the geometry of real submanifolds in complex space, and the role of symmetry and curvature in complex differential structures.

Written with clarity and rigor, this book is accessible to advanced graduate students and researchers alike. It serves not only as a snapshot of the state of the art but also as a guidepost for future inquiry. For anyone seeking to understand how the abstract beauty of complex variables intersects with the technical challenges of PDEs and the elegant structures of geometry, this volume provides both inspiration and a solid foundation.

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