Extension problems in complex and CR-geometry
Author(s)
Bibliographic Information
Extension problems in complex and CR-geometry
（Tesi = theses, 9）
Edizioni della Normale, Scuola Normale Superiore, c2008
- : pbk
Available at 9 libraries
-
Library, Research Institute for Mathematical Sciences, Kyoto University数研
: pbkSAR||14||1200009118059
Note
Bibliography: p. [141]-150
Description and Table of Contents
Description
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.
Table 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.
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