Stein Manifolds and Holomorphic Mappings

Stein Manifolds and Holomorphic Mappings
Author :
Publisher : Springer Science & Business Media
Total Pages : 501
Release :
ISBN-10 : 9783642222504
ISBN-13 : 3642222501
Rating : 4/5 (04 Downloads)

Synopsis Stein Manifolds and Holomorphic Mappings by : Franc Forstnerič

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.

Stein Manifolds and Holomorphic Mappings

Stein Manifolds and Holomorphic Mappings
Author :
Publisher : Springer
Total Pages : 569
Release :
ISBN-10 : 9783319610580
ISBN-13 : 3319610589
Rating : 4/5 (80 Downloads)

Synopsis Stein Manifolds and Holomorphic Mappings by : Franc Forstnerič

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.

From Holomorphic Functions to Complex Manifolds

From Holomorphic Functions to Complex Manifolds
Author :
Publisher : Springer Science & Business Media
Total Pages : 406
Release :
ISBN-10 : 9781468492736
ISBN-13 : 146849273X
Rating : 4/5 (36 Downloads)

Synopsis From Holomorphic Functions to Complex Manifolds by : Klaus Fritzsche

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.

From Stein to Weinstein and Back

From Stein to Weinstein and Back
Author :
Publisher : American Mathematical Soc.
Total Pages : 379
Release :
ISBN-10 : 9780821885338
ISBN-13 : 0821885332
Rating : 4/5 (38 Downloads)

Synopsis From Stein to Weinstein and Back by : Kai Cieliebak

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').

Theory of Stein Spaces

Theory of Stein Spaces
Author :
Publisher : Springer Science & Business Media
Total Pages : 269
Release :
ISBN-10 : 9781475743579
ISBN-13 : 1475743572
Rating : 4/5 (79 Downloads)

Synopsis Theory of Stein Spaces by : H. Grauert

1. The classical theorem of Mittag-Leffler was generalized to the case of several complex variables by Cousin in 1895. In its one variable version this says that, if one prescribes the principal parts of a merom orphic function on a domain in the complex plane e, then there exists a meromorphic function defined on that domain having exactly those principal parts. Cousin and subsequent authors could only prove the analogous theorem in several variables for certain types of domains (e. g. product domains where each factor is a domain in the complex plane). In fact it turned out that this problem can not be solved on an arbitrary domain in em, m ~ 2. The best known example for this is a "notched" bicylinder in 2 2 e . This is obtained by removing the set { (z , z ) E e 11 z I ~ !, I z 1 ~ !}, from 1 2 1 2 2 the unit bicylinder, ~ :={(z , z ) E e llz1

The Convenient Setting of Global Analysis

The Convenient Setting of Global Analysis
Author :
Publisher : American Mathematical Soc.
Total Pages : 631
Release :
ISBN-10 : 9780821807804
ISBN-13 : 0821807803
Rating : 4/5 (04 Downloads)

Synopsis The Convenient Setting of Global Analysis by : Andreas Kriegl

For graduate students and research mathematicians interested in global analysis and the analysis of manifolds, lays the foundations for a differential calculus in infinite dimensions and discusses applications in infinite-dimension differential geometry and global analysis not involving Sobolev completions and fixed-point theory. Shows how the notion of smoothness as mapping smooth curves to smooth curves coincides with all known reasonable concepts up to Frechet spaces. Then develops a calculus of holomorphic mappings, and another of real analytical mapping. Emphasizes regular infinite dimensional Lie groups. Annotation copyrighted by Book News, Inc., Portland, OR

Coherent Analytic Sheaves

Coherent Analytic Sheaves
Author :
Publisher : Springer Science & Business Media
Total Pages : 267
Release :
ISBN-10 : 9783642695827
ISBN-13 : 3642695825
Rating : 4/5 (27 Downloads)

Synopsis Coherent Analytic Sheaves by : H. Grauert

... Je mehr ich tiber die Principien der Functionentheorie nachdenke - und ich thue dies unablassig -, urn so fester wird meine Uberzeugung, dass diese auf dem Fundamente algebraischer Wahrheiten aufgebaut werden muss (WEIERSTRASS, Glaubensbekenntnis 1875, Math. Werke II, p. 235). 1. Sheaf Theory is a general tool for handling questions which involve local solutions and global patching. "La notion de faisceau s'introduit parce qu'il s'agit de passer de donnees 'locales' a l'etude de proprietes 'globales'" [CAR], p. 622. The methods of sheaf theory are algebraic. The notion of a sheaf was first introduced in 1946 by J. LERAY in a short note Eanneau d'homologie d'une representation, C.R. Acad. Sci. 222, 1366-68. Of course sheaves had occurred implicitly much earlier in mathematics. The "Monogene analytische Functionen", which K. WEIERSTRASS glued together from "Func tionselemente durch analytische Fortsetzung", are simply the connected components of the sheaf of germs of holomorphic functions on a RIEMANN surface*'; and the "ideaux de domaines indetermines", basic in the work of K. OKA since 1948 (cf. [OKA], p. 84, 107), are just sheaves of ideals of germs of holomorphic functions. Highly original contributions to mathematics are usually not appreciated at first. Fortunately H. CARTAN immediately realized the great importance of LERAY'S new abstract concept of a sheaf. In the polycopied notes of his Semina ire at the E.N.S

Advancements in Complex Analysis

Advancements in Complex Analysis
Author :
Publisher : Springer Nature
Total Pages : 538
Release :
ISBN-10 : 9783030401207
ISBN-13 : 3030401200
Rating : 4/5 (07 Downloads)

Synopsis Advancements in Complex Analysis by : Daniel Breaz

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.

Lectures on Symplectic Geometry

Lectures on Symplectic Geometry
Author :
Publisher : Springer
Total Pages : 240
Release :
ISBN-10 : 9783540453307
ISBN-13 : 354045330X
Rating : 4/5 (07 Downloads)

Synopsis Lectures on Symplectic Geometry by : Ana Cannas da Silva

The goal of these notes is to provide a fast introduction to symplectic geometry for graduate students with some knowledge of differential geometry, de Rham theory and classical Lie groups. This text addresses symplectomorphisms, local forms, contact manifolds, compatible almost complex structures, Kaehler manifolds, hamiltonian mechanics, moment maps, symplectic reduction and symplectic toric manifolds. It contains guided problems, called homework, designed to complement the exposition or extend the reader's understanding. There are by now excellent references on symplectic geometry, a subset of which is in the bibliography of this book. However, the most efficient introduction to a subject is often a short elementary treatment, and these notes attempt to serve that purpose. This text provides a taste of areas of current research and will prepare the reader to explore recent papers and extensive books on symplectic geometry where the pace is much faster. For this reprint numerous corrections and clarifications have been made, and the layout has been improved.

Period Mappings and Period Domains

Period Mappings and Period Domains
Author :
Publisher : Cambridge University Press
Total Pages : 577
Release :
ISBN-10 : 9781108422628
ISBN-13 : 1108422624
Rating : 4/5 (28 Downloads)

Synopsis Period Mappings and Period Domains by : James Carlson

An introduction to Griffiths' theory of period maps and domains, focused on algebraic, group-theoretic and differential geometric aspects.