The Geometric Theory Of Complex Variables

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The Geometric Theory Of Complex Variables

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Author : Peter V. Dovbush
language : en
Publisher: Springer Nature
Release Date : 2025-01-28

The Geometric Theory Of Complex Variables written by Peter V. Dovbush and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2025-01-28 with Mathematics categories.

This book provides the reader with a broad introduction to the geometric methodology in complex analysis. It covers both single and several complex variables, creating a dialogue between the two viewpoints. Regarded as one of the 'grand old ladies' of modern mathematics, complex analysis traces its roots back 500 years. The subject began to flourish with Carl Friedrich Gauss's thesis around 1800. The geometric aspects of the theory can be traced back to the Riemann mapping theorem around 1850, with a significant milestone achieved in 1938 with Lars Ahlfors's geometrization of complex analysis. These ideas inspired many other mathematicians to adopt this perspective, leading to the proliferation of geometric theory of complex variables in various directions, including Riemann surfaces, Teichmüller theory, complex manifolds, extremal problems, and many others. This book explores all these areas, with classical geometric function theory as its main focus. Its accessible and gentle approach makes it suitable for advanced undergraduate and graduate students seeking to understand the connections among topics usually scattered across numerous textbooks, as well as experienced mathematicians with an interest in this rich field.

Geometric Function Theory In Several Complex Variables

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Author : Junjirō Noguchi
language : en
Publisher: American Mathematical Soc.
Release Date : 1990

Geometric Function Theory In Several Complex Variables written by Junjirō Noguchi 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 1990 with Mathematics categories.

This is an expanded English-language version of a book by the same authors that originally appeared in the Japanese. The book serves two purposes. The first is to provide a self-contained and coherent account of recent developments in geometric function theory in several complex variables, aimed at those who have already mastered the basics of complex function theory and the elementary theory of differential and complex manifolds. The second goal is to present, in a self-contained way, fundamental descriptions of the theory of positive currents, plurisubharmonic functions, and meromorphic mappings, which are today indispensable in the analytic and geometric theories of complex functions of several variables. The book should prove useful for researchers and graduate students alike.

Geometric Theory Of Functions Of A Complex Variable

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Author : Gennadiĭ Mikhaĭlovich Goluzin
language : en
Publisher: American Mathematical Soc.
Release Date : 1969

Geometric Theory Of Functions Of A Complex Variable written by Gennadiĭ Mikhaĭlovich Goluzin 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 1969 with Functions of complex variables categories.

Geometric Function Theory

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Author : Steven G. Krantz
language : en
Publisher: Springer Science & Business Media
Release Date : 2006

Geometric Function Theory written by Steven G. Krantz 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 2006 with Mathematics categories.

* Presented from a geometric analytical viewpoint, this work addresses advanced topics in complex analysis that verge on modern areas of research * Methodically designed with individual chapters containing a rich collection of exercises, examples, and illustrations

Several Complex Variables Iii

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Author : G.M. Khenkin
language : en
Publisher: Springer Science & Business Media
Release Date : 1989-02-23

Several Complex Variables Iii written by G.M. Khenkin 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 1989-02-23 with Mathematics categories.

We consider the basic problems, notions and facts in the theory of entire functions of several variables, i. e. functions J(z) holomorphic in the entire n space en (i. e. JEH( 1 variables, as in the case n = 1, a central theme deals with questions of growth of functions and the distribu tion of their zeros. However, there are significant differences between the cases of one and several variables. In the first place there is the fact that for n 1 the zero set of an entire function is not discrete and therefore one has no analogue of a tool such as the canonical Weierstrass product, which is fundamental in the case n = 1. Second, for n> 1 there exist several different natural ways of exhausting the space

Geometric Theory Of Functions Of A Complex Variable

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Author : G. M. Goluzin
language : en
Publisher: American Mathematical Soc.
Release Date : 1969

Geometric Theory Of Functions Of A Complex Variable written by G. M. Goluzin 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 1969 with Mathematics categories.

This book is based on lectures on geometric function theory given by the author at Leningrad State University. It studies univalent conformal mapping of simply and multiply connected domains, conformal mapping of multiply connected domains onto a disk, applications of conformal mapping to the study of interior and boundary properties of analytic functions, and general questions of a geometric nature dealing with analytic functions. The second Russian edition upon which this English translation is based differs from the first mainly in the expansion of two chapters and in the addition of a long survey of more recent developments. The book is intended for readers who are already familiar with the basics of the theory of functions of one complex variable.

Lectures On The Theory Of Functions Of A Complex Variable

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Author :
language : en
Publisher:
Release Date : 1960

Lectures On The Theory Of Functions Of A Complex Variable written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1960 with categories.

Function Theory Of Several Complex Variables

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Author : Steven George Krantz
language : en
Publisher: American Mathematical Soc.
Release Date : 2001

Function Theory Of Several Complex Variables written by Steven George Krantz 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 2001 with Mathematics categories.

Emphasizing integral formulas, the geometric theory of pseudoconvexity, estimates, partial differential equations, approximation theory, inner functions, invariant metrics, and mapping theory, this title is intended for the student with a background in real and complex variable theory, harmonic analysis, and differential equations.

Several Complex Variables And Complex Geometry Part Ii

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Author : Eric Bedford
language : en
Publisher: American Mathematical Soc.
Release Date : 1991

Several Complex Variables And Complex Geometry Part Ii written by Eric Bedford 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 1991 with Mathematics categories.

Introduction To Geometric Function Theory Of Hypercomplex Variables

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Author : Sorin G. Gal
language : en
Publisher: Nova Publishers
Release Date : 2002

Introduction To Geometric Function Theory Of Hypercomplex Variables written by Sorin G. Gal and has been published by Nova Publishers this book supported file pdf, txt, epub, kindle and other format this book has been release on 2002 with Mathematics categories.

Introduction to Geometric Function Theory of Hypercomplex Variables