Geometry Of Holomorphic Mappings
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Geometry Of Holomorphic Mappings
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Author : Sergey Pinchuk
language : en
Publisher: Springer Nature
Release Date : 2023-10-16
Geometry Of Holomorphic Mappings written by Sergey Pinchuk and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-10-16 with Mathematics categories.
This monograph explores the problem of boundary regularity and analytic continuation of holomorphic mappings between domains in complex Euclidean spaces. Many important methods and techniques in several complex variables have been developed in connection with these questions, and the goal of this book is to introduce the reader to some of these approaches and to demonstrate how they can be used in the context of boundary properties of holomorphic maps. The authors present substantial results concerning holomorphic mappings in several complex variables with improved and often simplified proofs. Emphasis is placed on geometric methods, including the Kobayashi metric, the Scaling method, Segre varieties, and the Reflection principle. Geometry of Holomorphic Mappings will provide a valuable resource for PhD students in complex analysis and complex geometry; it will also be of interest to researchers in these areas as a reference.
Hyperbolic Manifolds And Holomorphic Mappings
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Author : Shoshichi Kobayashi
language : en
Publisher: World Scientific
Release Date : 2005
Hyperbolic Manifolds And Holomorphic Mappings written by Shoshichi Kobayashi and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005 with Mathematics categories.
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.
Stein Manifolds And Holomorphic Mappings
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Author : Franc Forstnerič
language : en
Publisher: Springer Science & Business Media
Release Date : 2011-08-27
Stein Manifolds And Holomorphic Mappings written by Franc Forstnerič and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-08-27 with Mathematics categories.
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.
Numerical Range Of Holomorphic Mappings And Applications
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Author : Mark Elin
language : en
Publisher: Springer
Release Date : 2019-03-11
Numerical Range Of Holomorphic Mappings And Applications written by Mark Elin and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-03-11 with Mathematics categories.
This book describes recent developments as well as some classical results regarding holomorphic mappings. The book starts with a brief survey of the theory of semigroups of linear operators including the Hille-Yosida and the Lumer-Phillips theorems. The numerical range and the spectrum of closed densely defined linear operators are then discussed in more detail and an overview of ergodic theory is presented. The analytic extension of semigroups of linear operators is also discussed. The recent study of the numerical range of composition operators on the unit disk is mentioned. Then, the basic notions and facts in infinite dimensional holomorphy and hyperbolic geometry in Banach and Hilbert spaces are presented, L. A. Harris' theory of the numerical range of holomorphic mappings is generalized, and the main properties of the so-called quasi-dissipative mappings and their growth estimates are studied. In addition, geometric and quantitative analytic aspects of fixed point theory are discussed. A special chapter is devoted to applications of the numerical range to diverse geometric and analytic problems.
Topology On Spaces Of Holomorphic Mappings
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Author : Leopoldo Nachbin
language : en
Publisher:
Release Date : 1969
Topology On Spaces Of Holomorphic Mappings written by Leopoldo Nachbin and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1969 with Analytic functions categories.
Several Complex Variables And The Geometry Of Real Hypersurfaces
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Author : John P. D'Angelo
language : en
Publisher: Routledge
Release Date : 2019-07-16
Several Complex Variables And The Geometry Of Real Hypersurfaces written by John P. D'Angelo and has been published by Routledge this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-07-16 with Mathematics categories.
Several Complex Variables and the Geometry of Real Hypersurfaces covers a wide range of information from basic facts about holomorphic functions of several complex variables through deep results such as subelliptic estimates for the ?-Neumann problem on pseudoconvex domains with a real analytic boundary. The book focuses on describing the geometry of a real hypersurface in a complex vector space by understanding its relationship with ambient complex analytic varieties. You will learn how to decide whether a real hypersurface contains complex varieties, how closely such varieties can contact the hypersurface, and why it's important. The book concludes with two sets of problems: routine problems and difficult problems (many of which are unsolved). Principal prerequisites for using this book include a thorough understanding of advanced calculus and standard knowledge of complex analysis in one variable. Several Complex Variables and the Geometry of Real Hypersurfaces will be a useful text for advanced graduate students and professionals working in complex analysis.
Distribution Of Values Of Holomorphic Mappings
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Author : Boris Vladimirovich Shabat
language : en
Publisher: American Mathematical Soc.
Release Date : 1985-12-31
Distribution Of Values Of Holomorphic Mappings written by Boris Vladimirovich Shabat and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 1985-12-31 with Mathematics categories.
A vast literature has grown up around the value distribution theory of meromorphic functions, synthesized by Rolf Nevanlinna in the 1920s and singled out by Hermann Weyl as one of the greatest mathematical achievements of this century. The multidimensional aspect, involving the distribution of inverse images of analytic sets under holomorphic mappings of complex manifolds, has not been fully treated in the literature. This volume thus provides a valuable introduction to multivariate value distribution theory and a survey of some of its results, rich in relations to both algebraic and differential geometry and surely one of the most important branches of the modern geometric theory of functions of a complex variable. Since the book begins with preparatory material from the contemporary geometric theory of functions, only a familiarity with the elements of multidimensional complex analysis is necessary background to understand the topic. After proving the two main theorems of value distribution theory, the author goes on to investigate further the theory of holomorphic curves and to provide generalizations and applications of the main theorems, focusing chiefly on the work of Soviet mathematicians.
Holomorphic Maps And Invariant Distances
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Author :
language : en
Publisher: Elsevier
Release Date : 1980-01-01
Holomorphic Maps And Invariant Distances written by and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 1980-01-01 with Mathematics categories.
Holomorphic Maps and Invariant Distances
Invariant Theory In Cauchy Riemann Geometry And Applications To The Study Of Holomorphic Mappings
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Author : Yuan Zhang
language : en
Publisher:
Release Date : 2009
Invariant Theory In Cauchy Riemann Geometry And Applications To The Study Of Holomorphic Mappings written by Yuan Zhang and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009 with Cauchy-Riemann equations categories.
In this dissertation, proper holomorphic maps between some types of CR manifolds have been studied. For non-degenerate holomorphic Segre maps between Hn and HN, the complexifications of Heisenberg hypersurfaces, we show that they possess a partial rigidity property when N [less than/equal to] 2n - 2. As an application under the same assumption, we prove that the holomorphic Segre non-transversality for these maps propagates along Segre varieties. this propagation property fails when N> 2n - 2. For any proper rational holomorphic map between complex balls, we derive a simple and explicit criterion when it is equivalent to a holomorphic polynomial map. This criterion is used to show that proper rational holomorphic maps from B2 into BN of degree two are equivalent to polynomial maps. For general smooth CR embeddings from a Levi non-degenerate hypersurface into another one with the same signature, a monotonicity property of the Chern-Moser-Weyl curvature along directions in the null space of the Levi-form has been obtained.
Two Reports On Harmonic Maps
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Author : James Eells
language : en
Publisher: World Scientific
Release Date : 1995
Two Reports On Harmonic Maps written by James Eells and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 1995 with Mathematics categories.
Harmonic maps between Riemannian manifolds are solutions of systems of nonlinear partial differential equations which appear in different contexts of differential geometry. They include holomorphic maps, minimal surfaces, å-models in physics. Recently, they have become powerful tools in the study of global properties of Riemannian and Khlerian manifolds.A standard reference for this subject is a pair of Reports, published in 1978 and 1988 by James Eells and Luc Lemaire.This book presents these two reports in a single volume with a brief supplement reporting on some recent developments in the theory. It is both an introduction to the subject and a unique source of references, providing an organized exposition of results spread throughout more than 800 papers.