Extension Problems in Complex and CR-Geometry

1. Auflage 2008
ISBN: 978-88-7642-338-3
Verlag: Scuola Normale Superiore

Buch, Englisch, 150 Seiten, Format (B × H): 154 mm x 242 mm, Gewicht: 360 g

Reihe: Theses (Scuola Normale Superiore)

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.

Zielgruppe

Research

Autoren/Hrsg.

Saracco, Alberto

Fachgebiete

• Mathematik | Informatik Mathematik Geometrie Algebraische Geometrie
• Mathematik | Informatik Mathematik Mathematische Analysis Funktionentheorie, Komplexe Analysis

Inhaltsverzeichnis

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.