Stein Manifolds and Holomorphic Mappings
Title | Stein Manifolds and Holomorphic Mappings PDF eBook |
Author | Franc Forstnerič |
Publisher | Springer Science & Business Media |
Pages | 501 |
Release | 2011-08-27 |
Genre | Mathematics |
ISBN | 3642222501 |
The main theme of this book is the homotopy principle for holomorphic mappings from Stein manifolds to the newly introduced class of Oka manifolds. The book contains the first complete account of Oka-Grauert theory and its modern extensions, initiated by Mikhail Gromov and developed in the last decade by the author and his collaborators. Included is the first systematic presentation of the theory of holomorphic automorphisms of complex Euclidean spaces, a survey on Stein neighborhoods, connections between the geometry of Stein surfaces and Seiberg-Witten theory, and a wide variety of applications ranging from classical to contemporary.
Holomorphic Extension on Stein Manifolds
Title | Holomorphic Extension on Stein Manifolds PDF eBook |
Author | Tongde Zhong |
Publisher | |
Pages | 22 |
Release | 1987 |
Genre | |
ISBN |
Stein Manifolds and Holomorphic Mappings
Title | Stein Manifolds and Holomorphic Mappings PDF eBook |
Author | Franc Forstnerič |
Publisher | Springer |
Pages | 569 |
Release | 2017-09-05 |
Genre | Mathematics |
ISBN | 3319610589 |
This book, now in a carefully revised second edition, provides an up-to-date account of Oka theory, including the classical Oka-Grauert theory and the wide array of applications to the geometry of Stein manifolds. Oka theory is the field of complex analysis dealing with global problems on Stein manifolds which admit analytic solutions in the absence of topological obstructions. The exposition in the present volume focuses on the notion of an Oka manifold introduced by the author in 2009. It explores connections with elliptic complex geometry initiated by Gromov in 1989, with the Andersén-Lempert theory of holomorphic automorphisms of complex Euclidean spaces and of Stein manifolds with the density property, and with topological methods such as homotopy theory and the Seiberg-Witten theory. Researchers and graduate students interested in the homotopy principle in complex analysis will find this book particularly useful. It is currently the only work that offers a comprehensive introduction to both the Oka theory and the theory of holomorphic automorphisms of complex Euclidean spaces and of other complex manifolds with large automorphism groups.
Extension of Holomorphic Functions
Title | Extension of Holomorphic Functions PDF eBook |
Author | Marek Jarnicki |
Publisher | Walter de Gruyter GmbH & Co KG |
Pages | 455 |
Release | 2020-05-05 |
Genre | Mathematics |
ISBN | 3110627698 |
This second extended edition of the classic reference on the extension problem of holomorphic functions in pluricomplex analysis contains a wealth of additional material, organized under the original chapter structure, and covers in a self-contained way all new and recent developments and theorems that appeared since the publication of the first edition about twenty years ago.
From Holomorphic Functions to Complex Manifolds
Title | From Holomorphic Functions to Complex Manifolds PDF eBook |
Author | Klaus Fritzsche |
Publisher | Springer Science & Business Media |
Pages | 406 |
Release | 2012-12-06 |
Genre | Mathematics |
ISBN | 146849273X |
This introduction to the theory of complex manifolds covers the most important branches and methods in complex analysis of several variables while completely avoiding abstract concepts involving sheaves, coherence, and higher-dimensional cohomology. Only elementary methods such as power series, holomorphic vector bundles, and one-dimensional cocycles are used. Each chapter contains a variety of examples and exercises.
Extending Holomorphic Mappings from Subvarieties in Stein Manifolds
Title | Extending Holomorphic Mappings from Subvarieties in Stein Manifolds PDF eBook |
Author | Franc Forstnerič |
Publisher | |
Pages | 13 |
Release | 2004 |
Genre | Forschungsbericht |
ISBN |
Some Extension Theorems for Regular Maps of Stein Manifolds
Title | Some Extension Theorems for Regular Maps of Stein Manifolds PDF eBook |
Author | Chester Cornelius Seabury |
Publisher | |
Pages | 114 |
Release | 1973 |
Genre | Manifolds (Mathematics) |
ISBN |