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. Presents a large survey on the broad subject of extension in complex analysis and CR geometry Endowed with a very extensive bibliography INDICE: 1. Introduction.- 2. Classical extension theorems in one and several complex variables.- 3. Extension of CR-functions up to a Levi-flat boundaryand 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 analyticvarieties.- 8. Semi-local extension of maximally complex submanifolds.
- ISBN: 978-88-7642-338-3
- Editorial: Birkhaüser
- Encuadernacion: Rústica
- Páginas: 150
- Fecha Publicación: 01/11/2008
- Nº Volúmenes: 1
- Idioma: Inglés