Conformal Mapping On Riemann Surfaces

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Conformal Mapping On Riemann Surfaces

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Author : Harvey Cohn
language : en
Publisher:
Release Date : 1967

Conformal Mapping On Riemann Surfaces written by Harvey Cohn and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1967 with Conformal mapping categories.

Quasiconformal Mappings And Riemann Surfaces

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Author : Samuil Leĭbovich Krushkalʹ
language : en
Publisher: Winston Publishing
Release Date : 1979

Quasiconformal Mappings And Riemann Surfaces written by Samuil Leĭbovich Krushkalʹ and has been published by Winston Publishing this book supported file pdf, txt, epub, kindle and other format this book has been release on 1979 with Mathematics categories.

Complex Analysis Riemann Surfaces And Integrable Systems

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Author : Sergey M. Natanzon
language : en
Publisher: Springer Nature
Release Date : 2020-01-03

Complex Analysis Riemann Surfaces And Integrable Systems written by Sergey M. Natanzon and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-01-03 with Mathematics categories.

This book is devoted to classical and modern achievements in complex analysis. In order to benefit most from it, a first-year university background is sufficient; all other statements and proofs are provided. We begin with a brief but fairly complete course on the theory of holomorphic, meromorphic, and harmonic functions. We then present a uniformization theory, and discuss a representation of the moduli space of Riemann surfaces of a fixed topological type as a factor space of a contracted space by a discrete group. Next, we consider compact Riemann surfaces and prove the classical theorems of Riemann-Roch, Abel, Weierstrass, etc. We also construct theta functions that are very important for a range of applications. After that, we turn to modern applications of this theory. First, we build the (important for mathematics and mathematical physics) Kadomtsev-Petviashvili hierarchy and use validated results to arrive at important solutions to these differential equations. We subsequently use the theory of harmonic functions and the theory of differential hierarchies to explicitly construct a conformal mapping that translates an arbitrary contractible domain into a standard disk – a classical problem that has important applications in hydrodynamics, gas dynamics, etc. The book is based on numerous lecture courses given by the author at the Independent University of Moscow and at the Mathematics Department of the Higher School of Economics.

Riemann Surfaces

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Author : Lars Valerian Ahlfors
language : en
Publisher: Princeton University Press
Release Date : 2015-12-08

Riemann Surfaces written by Lars Valerian Ahlfors and has been published by Princeton University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-12-08 with Mathematics categories.

The theory of Riemann surfaces has a geometric and an analytic part. The former deals with the axiomatic definition of a Riemann surface, methods of construction, topological equivalence, and conformal mappings of one Riemann surface on another. The analytic part is concerned with the existence and properties of functions that have a special character connected with the conformal structure, for instance: subharmonic, harmonic, and analytic functions. Originally published in 1960. The Princeton Legacy Library uses the latest print-on-demand technology to again make available previously out-of-print books from the distinguished backlist of Princeton University Press. These editions preserve the original texts of these important books while presenting them in durable paperback and hardcover editions. The goal of the Princeton Legacy Library is to vastly increase access to the rich scholarly heritage found in the thousands of books published by Princeton University Press since its founding in 1905.

The Conformal Mapping Of Simply Connected Riemann Surfaces Ii

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Author : Maurice Heins
language : en
Publisher:
Release Date : 1957

The Conformal Mapping Of Simply Connected Riemann Surfaces Ii written by Maurice Heins and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1957 with Riemann surfaces categories.

Compact Riemann Surfaces

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Author : Jürgen Jost
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-04-17

Compact Riemann Surfaces written by Jürgen Jost 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 2013-04-17 with Mathematics categories.

Although Riemann surfaces are a time-honoured field, this book is novel in its broad perspective that systematically explores the connection with other fields of mathematics. It can serve as an introduction to contemporary mathematics as a whole as it develops background material from algebraic topology, differential geometry, the calculus of variations, elliptic PDE, and algebraic geometry. It is unique among textbooks on Riemann surfaces in including an introduction to Teichmüller theory. The analytic approach is likewise new as it is based on the theory of harmonic maps.

Quasiconformal Mappings Riemann Surfaces And Teichmuller Spaces

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Author : Yunping Jiang
language : en
Publisher: American Mathematical Soc.
Release Date : 2012

Quasiconformal Mappings Riemann Surfaces And Teichmuller Spaces written by Yunping Jiang 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 2012 with Mathematics categories.

This volume contains the proceedings of the AMS Special Session on Quasiconformal Mappings, Riemann Surfaces, and Teichmuller Spaces, held in honor of Clifford J. Earle, from October 2-3, 2010, in Syracuse, New York. This volume includes a wide range of papers on Teichmuller theory and related areas. It provides a broad survey of the present state of research and the applications of quasiconformal mappings, Riemann surfaces, complex dynamical systems, Teichmuller theory, and geometric function theory. The papers in this volume reflect the directions of research in different aspects of these fields and also give the reader an idea of how Teichmuller theory intersects with other areas of mathematics.

Conformal Mapping

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Author : Zeev Nehari
language : en
Publisher: Courier Corporation
Release Date : 1975-01-01

Conformal Mapping written by Zeev Nehari and has been published by Courier Corporation this book supported file pdf, txt, epub, kindle and other format this book has been release on 1975-01-01 with Mathematics categories.

Conformal mapping is a field in which pure and applied mathematics are both involved. This book tries to bridge the gulf that many times divides these two disciplines by combining the theoretical and practical approaches to the subject. It will interest the pure mathematician, engineer, physicist, and applied mathematician. The potential theory and complex function theory necessary for a full treatment of conformal mapping are developed in the first four chapters, so the reader needs no other text on complex variables. These chapters cover harmonic functions, analytic functions, the complex integral calculus, and families of analytic functions. Included here are discussions of Green's formula, the Poisson formula, the Cauchy-Riemann equations, Cauchy's theorem, the Laurent series, and the Residue theorem. The final three chapters consider in detail conformal mapping of simply-connected domains, mapping properties of special functions, and conformal mapping of multiply-connected domains. The coverage here includes such topics as the Schwarz lemma, the Riemann mapping theorem, the Schwarz-Christoffel formula, univalent functions, the kernel function, elliptic functions, univalent functions, the kernel function, elliptic functions, the Schwarzian s-functions, canonical domains, and bounded functions. There are many problems and exercises, making the book useful for both self-study and classroom use. The author, former professor of mathematics at Carnegie-Mellon University, has designed the book as a semester's introduction to functions of a complex variable followed by a one-year graduate course in conformal mapping. The material is presented simply and clearly, and the only prerequisite is a good working knowledge of advanced calculus.

Principles Of Complex Analysis

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Author : Serge Lvovski
language : en
Publisher: Springer Nature
Release Date : 2020-09-26

Principles Of Complex Analysis written by Serge Lvovski and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-09-26 with Mathematics categories.

This is a brief textbook on complex analysis intended for the students of upper undergraduate or beginning graduate level. The author stresses the aspects of complex analysis that are most important for the student planning to study algebraic geometry and related topics. The exposition is rigorous but elementary: abstract notions are introduced only if they are really indispensable. This approach provides a motivation for the reader to digest more abstract definitions (e.g., those of sheaves or line bundles, which are not mentioned in the book) when he/she is ready for that level of abstraction indeed. In the chapter on Riemann surfaces, several key results on compact Riemann surfaces are stated and proved in the first nontrivial case, i.e. that of elliptic curves.

Conformal Representation

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Author : Constantin Caratheodory
language : en
Publisher: Courier Corporation
Release Date : 1998-01-01

Conformal Representation written by Constantin Caratheodory and has been published by Courier Corporation this book supported file pdf, txt, epub, kindle and other format this book has been release on 1998-01-01 with Mathematics categories.

Comprehensive introduction discusses the Möbius transformation, non-Euclidean geometry, elementary transformations, Schwarz's Lemma, transformation of the frontier and closed surfaces, and the general theorem of uniformization. Detailed proofs.