Stein Manifolds And Holomorphic Mappings

Author : Franc Forstnerič
Publisher : Springer Science & Business Media
Page : 492 pages
File Size : 52,7 Mb
Release : 2011-08-27
Category : Mathematics
ISBN : 9783642222504

Get Book

Stein Manifolds and Holomorphic Mappings by Franc Forstnerič Pdf

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.

Author : Franc Forstnerič
Publisher : Springer
Page : 569 pages
File Size : 44,8 Mb
Release : 2017-09-05
Category : Mathematics
ISBN : 9783319610580

Get Book

Stein Manifolds and Holomorphic Mappings by Franc Forstnerič Pdf

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.

Author : Eric Zeisel
Publisher : Unknown
Page : 122 pages
File Size : 40,9 Mb
Release : 1995
Category : Electronic
ISBN : STANFORD:36105009717898

Get Book

Maps of Stein Manifolds Without Triple Points by Eric Zeisel Pdf

Author : Klaus Fritzsche,Hans Grauert
Publisher : Springer Science & Business Media
Page : 406 pages
File Size : 54,9 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781468492736

Get Book

From Holomorphic Functions to Complex Manifolds by Klaus Fritzsche,Hans Grauert Pdf

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.

Author : Chester Cornelius Seabury
Publisher : Unknown
Page : 114 pages
File Size : 46,5 Mb
Release : 1973
Category : Manifolds (Mathematics)
ISBN : STANFORD:36105025646246

Get Book

Some Extension Theorems for Regular Maps of Stein Manifolds by Chester Cornelius Seabury Pdf

Author : Donald A. Eisenman
Publisher : American Mathematical Soc.
Page : 84 pages
File Size : 40,9 Mb
Release : 1970
Category : Analytic functions
ISBN : 9780821812969

Get Book

Intrinsic Measures on Complex Manifolds and Holomorphic Mappings by Donald A. Eisenman Pdf

Author : Daniel Breaz,Michael Th. Rassias
Publisher : Springer Nature
Page : 538 pages
File Size : 45,9 Mb
Release : 2020-05-12
Category : Mathematics
ISBN : 9783030401207

Get Book

Advancements in Complex Analysis by Daniel Breaz,Michael Th. Rassias Pdf

The contributions to this volume are devoted to a discussion of state-of-the-art research and treatment of problems of a wide spectrum of areas in complex analysis ranging from pure to applied and interdisciplinary mathematical research. Topics covered include: holomorphic approximation, hypercomplex analysis, special functions of complex variables, automorphic groups, zeros of the Riemann zeta function, Gaussian multiplicative chaos, non-constant frequency decompositions, minimal kernels, one-component inner functions, power moment problems, complex dynamics, biholomorphic cryptosystems, fermionic and bosonic operators. The book will appeal to graduate students and research mathematicians as well as to physicists, engineers, and scientists, whose work is related to the topics covered.

Author : Shoshichi Kobayashi
Publisher : World Scientific Publishing Company
Page : 160 pages
File Size : 48,9 Mb
Release : 2005-11-02
Category : Mathematics
ISBN : 9789813101937

Get Book

Hyperbolic Manifolds and Holomorphic Mappings by Shoshichi Kobayashi Pdf

The first edition of this influential book, published in 1970, opened up a completely new field of invariant metrics and hyperbolic manifolds. The large number of papers on the topics covered by the book written since its appearance led Mathematical Reviews to create two new subsections “invariant metrics and pseudo-distances” and “hyperbolic complex manifolds” within the section “holomorphic mappings”. The invariant distance introduced in the first edition is now called the “Kobayashi distance”, and the hyperbolicity in the sense of this book is called the “Kobayashi hyperbolicity” to distinguish it from other hyperbolicities. This book continues to serve as the best introduction to hyperbolic complex analysis and geometry and is easily accessible to students since very little is assumed. The new edition adds comments on the most recent developments in the field.

Author : Kai Cieliebak,Y. Eliashberg
Publisher : American Mathematical Soc.
Page : 379 pages
File Size : 47,9 Mb
Release : 2012
Category : Mathematics
ISBN : 9780821885338

Get Book

From Stein to Weinstein and Back by Kai Cieliebak,Y. Eliashberg Pdf

This book is devoted to the interplay between complex and symplectic geometry in affine complex manifolds. Affine complex (a.k.a. Stein) manifolds have canonically built into them symplectic geometry which is responsible for many phenomena in complex geometry and analysis. The goal of the book is the exploration of this symplectic geometry (the road from 'Stein to Weinstein') and its applications in the complex geometric world of Stein manifolds (the road 'back').

Author : Antonio Alarcón,Franc Forstnerič,Francisco J. López
Publisher : Springer Nature
Page : 430 pages
File Size : 45,8 Mb
Release : 2021-03-10
Category : Mathematics
ISBN : 9783030690564

Get Book

Minimal Surfaces from a Complex Analytic Viewpoint by Antonio Alarcón,Franc Forstnerič,Francisco J. López Pdf

This monograph offers the first systematic treatment of the theory of minimal surfaces in Euclidean spaces by complex analytic methods, many of which have been developed in recent decades as part of the theory of Oka manifolds (the h-principle in complex analysis). It places particular emphasis on the study of the global theory of minimal surfaces with a given complex structure. Advanced methods of holomorphic approximation, interpolation, and homotopy classification of manifold-valued maps, along with elements of convex integration theory, are implemented for the first time in the theory of minimal surfaces. The text also presents newly developed methods for constructing minimal surfaces in minimally convex domains of Rn, based on the Riemann–Hilbert boundary value problem adapted to minimal surfaces and holomorphic null curves. These methods also provide major advances in the classical Calabi–Yau problem, yielding in particular minimal surfaces with the conformal structure of any given bordered Riemann surface. Offering new directions in the field and several challenging open problems, the primary audience of the book are researchers (including postdocs and PhD students) in differential geometry and complex analysis. Although not primarily intended as a textbook, two introductory chapters surveying background material and the classical theory of minimal surfaces also make it suitable for preparing Masters or PhD level courses.

Author : W. Stoll
Publisher : Springer
Page : 269 pages
File Size : 53,9 Mb
Release : 2006-11-15
Category : Mathematics
ISBN : 9783540362876

Get Book

Value Distribution of Holomorphic Maps into Compact Complex Manifolds by W. Stoll Pdf

Author : Andrew D. Lewis
Publisher : Springer Nature
Page : 323 pages
File Size : 41,7 Mb
Release : 2023-12-09
Category : Mathematics
ISBN : 9783031379130

Get Book

Geometric Analysis on Real Analytic Manifolds by Andrew D. Lewis Pdf

This monograph provides some useful tools for performing global geometric analysis on real analytic manifolds. At the core of the methodology of the book is a variety of descriptions for the topologies for the space of real analytic sections of a real analytic vector bundle and for the space of real analytic mappings between real analytic manifolds. Among the various descriptions for these topologies is a development of geometric seminorms for the space of real analytic sections. To illustrate the techniques in the book, a number of fundamental constructions in differential geometry are shown to induce continuous mappings on spaces of real analytic sections and mappings. Aimed at researchers at the level of Doctoral students and above, the book introduces the reader to the challenges and opportunities of real analytic analysis and geometry.

Author : Shoshichi Kobayashi
Publisher : Unknown
Page : 192 pages
File Size : 46,6 Mb
Release : 1970
Category : Mathematics
ISBN : UOM:39015015695649

Get Book

Hyperbolic Manifolds and Holomorphic Mappings by Shoshichi Kobayashi Pdf

Author : Daniele Angella,Costantino Medori,Adriano Tomassini
Publisher : Springer
Page : 262 pages
File Size : 41,7 Mb
Release : 2017-10-12
Category : Mathematics
ISBN : 9783319629148

Get Book

Complex and Symplectic Geometry by Daniele Angella,Costantino Medori,Adriano Tomassini Pdf

This book arises from the INdAM Meeting "Complex and Symplectic Geometry", which was held in Cortona in June 2016. Several leading specialists, including young researchers, in the field of complex and symplectic geometry, present the state of the art of their research on topics such as the cohomology of complex manifolds; analytic techniques in Kähler and non-Kähler geometry; almost-complex and symplectic structures; special structures on complex manifolds; and deformations of complex objects. The work is intended for researchers in these areas.

Author : Jisoo Byun,Hong Rae Cho,Sung Yeon Kim,Kang-Hyurk Lee,Jong-Do Park
Publisher : Springer
Page : 361 pages
File Size : 53,7 Mb
Release : 2018-09-08
Category : Mathematics
ISBN : 9789811316722

Get Book

Geometric Complex Analysis by Jisoo Byun,Hong Rae Cho,Sung Yeon Kim,Kang-Hyurk Lee,Jong-Do Park Pdf

The KSCV Symposium, the Korean Conference on Several Complex Variables, started in 1997 in an effort to promote the study of complex analysis and geometry. Since then, the conference met semi-regularly for about 10 years and then settled on being held biannually. The sixth and tenth conferences were held in 2002 and 2014 as satellite conferences to the Beijing International Congress of Mathematicians (ICM) and the Seoul ICM, respectively. The purpose of the KSCV Symposium is to organize the research talks of many leading scholars in the world, to provide an opportunity for communication, and to promote new researchers in this field.