Extension problems in complex and CR-geometry

This book is both a survey of some aspects of extension problems in Complex Analysis and Geometry and a collection of results by the author. After recalling the preliminary and necessary notions of complex analysis, the survey focuses on extension of holomorphic functions (filling both compact and non-compact holes), on the reflection principle, on extension results via cohomology vanishing, and on the boundary problem. The last two subjects include detailed results by the author on non-compact extension: the cohomology of semi q-coronae and the unbounded boundary problem.

List of contents

1. Introduction.- 2. Classical extension theorems in one and several complex variables.- 3. Extension of CR-functions up to a Levi-flat boundary and of holomorphic maps.- 4. Cohomology vanishing and extension problems for semi q-coronae.- 5. Cohomology of semi 1-coronae and extension of analytic subsets.- 6. The boundary problem.- 7. Non-compact boundaries of complex analytic varieties.- 8. Semi-local extension of maximally complex submanifolds.

Product details

• Authors: Alberto Saracco
• Publisher: Springer, Berlin
• Languages: English
• Product format: Paperback / Softback
• Released: 29.12.2008
• EAN: 9788876423383
• ISBN: 978-88-7642-338-3
• No. of pages: 150
• Illustrations: 150 p.
• Series: Publications of the Scuola Normale Superiore; Theses (Scuola Normale Superiore)
• Subject: Natural sciences, medicine, IT, technology > Mathematics > Analysis