Classification Theory Of Riemann Surfaces

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Classification Theory Of Riemann Surfaces

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Author : Leo Sario
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06

Classification Theory Of Riemann Surfaces written by Leo Sario 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 2012-12-06 with Mathematics categories.

The purpose of the present monograph is to systematically develop a classification theory of Riemann surfaces. Some first steps will also be taken toward a classification of Riemannian spaces. Four phases can be distinguished in the chronological background: the type problem; general classification; compactifications; and extension to higher dimensions. The type problem evolved in the following somewhat overlapping steps: the Riemann mapping theorem, the classical type problem, and the existence of Green's functions. The Riemann mapping theorem laid the foundation to classification theory: there are only two conformal equivalence classes of (noncompact) simply connected regions. Over half a century of efforts by leading mathematicians went into giving a rigorous proof of the theorem: RIEMANN, WEIERSTRASS, SCHWARZ, NEUMANN, POINCARE, HILBERT, WEYL, COURANT, OSGOOD, KOEBE, CARATHEODORY, MONTEL. The classical type problem was to determine whether a given simply connected covering surface of the plane is conformally equivalent to the plane or the disko The problem was in the center of interest in the thirties and early forties, with AHLFORS, KAKUTANI, KOBAYASHI, P. MYRBERG, NEVANLINNA, SPEISER, TEICHMÜLLER and others obtaining incisive specific results. The main problem of finding necessary and sufficient conditions remains, however, unsolved.

Galois Theory Coverings And Riemann Surfaces

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Author : Askold Khovanskii
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-09-11

Galois Theory Coverings And Riemann Surfaces written by Askold Khovanskii 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 2013-09-11 with Mathematics categories.

The first part of this book provides an elementary and self-contained exposition of classical Galois theory and its applications to questions of solvability of algebraic equations in explicit form. The second part describes a surprising analogy between the fundamental theorem of Galois theory and the classification of coverings over a topological space. The third part contains a geometric description of finite algebraic extensions of the field of meromorphic functions on a Riemann surface and provides an introduction to the topological Galois theory developed by the author. All results are presented in the same elementary and self-contained manner as classical Galois theory, making this book both useful and interesting to readers with a variety of backgrounds in mathematics, from advanced undergraduate students to researchers.

Dessins D Enfants On Riemann Surfaces

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Author : Gareth A. Jones
language : en
Publisher: Springer
Release Date : 2016-03-23

Dessins D Enfants On Riemann Surfaces written by Gareth A. Jones and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-03-23 with Mathematics categories.

This volume provides an introduction to dessins d'enfants and embeddings of bipartite graphs in compact Riemann surfaces. The first part of the book presents basic material, guiding the reader through the current field of research. A key point of the second part is the interplay between the automorphism groups of dessins and their Riemann surfaces, and the action of the absolute Galois group on dessins and their algebraic curves. It concludes by showing the links between the theory of dessins and other areas of arithmetic and geometry, such as the abc conjecture, complex multiplication and Beauville surfaces. Dessins d'Enfants on Riemann Surfaces will appeal to graduate students and all mathematicians interested in maps, hypermaps, Riemann surfaces, geometric group actions, and arithmetic.

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.

Hardy Classes On Riemann Surfaces

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Author : Maurice Heins
language : en
Publisher: Springer
Release Date : 2006-11-14

Hardy Classes On Riemann Surfaces written by Maurice Heins and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-11-14 with Mathematics categories.

A Primer On Riemann Surfaces

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Author : A. F. Beardon
language : en
Publisher: CUP Archive
Release Date : 1984-10-18

A Primer On Riemann Surfaces written by A. F. Beardon and has been published by CUP Archive this book supported file pdf, txt, epub, kindle and other format this book has been release on 1984-10-18 with Mathematics categories.

Hardy Classes On Infinitely Connected Riemann Surfaces

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Author : M. Hasumi
language : en
Publisher: Springer
Release Date : 2006-11-14

Hardy Classes On Infinitely Connected Riemann Surfaces written by M. Hasumi and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-11-14 with Mathematics categories.

Riemann Surfaces And Related Topics Am 97 Volume 97

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Author : Irwin Kra
language : en
Publisher: Princeton University Press
Release Date : 2016-03-02

Riemann Surfaces And Related Topics Am 97 Volume 97 written by Irwin Kra 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 2016-03-02 with Mathematics categories.

A classic treatment of Riemann surfaces from the acclaimed Annals of Mathematics Studies series Princeton University Press is proud to have published the Annals of Mathematics Studies since 1940. One of the oldest and most respected series in science publishing, it has included many of the most important and influential mathematical works of the twentieth century. The series continues this tradition as Princeton University Press publishes the major works of the twenty-first century. To mark the continued success of the series, all books are available in paperback and as ebooks.

Classical Complex Analysis

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Author : I-Hsiung Lin
language : en
Publisher: World Scientific
Release Date : 2011

Classical Complex Analysis written by I-Hsiung Lin and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011 with Mathematics categories.

Classical Complex Analysis provides an introduction to one of the remarkable branches of exact science, with an emphasis on the geometric aspects of analytic functions. This volume begins with a geometric description of what a complex number is, followed by a detailed account of algebraic, analytic and geometric properties of standard complex-valued functions. Geometric properties of analytic functions are then developed and described In detail, and various applications of residues are Included; analytic continuation is also introduced. --Book Jacket.

Journal Of Fourier Analysis And Applications Special Issue

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Author : John J. Benedetto
language : en
Publisher: CRC Press
Release Date : 2020-03-10

Journal Of Fourier Analysis And Applications Special Issue written by John J. Benedetto and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-03-10 with Mathematics categories.

The Journal of Fourier Analysis and Applications is a journal of the mathematical sciences devoted to Fourier analysis and its applications. The subject of Fourier analysis has had a major impact on the development of mathematics, on the understanding of many engineering and scientific phenomena, and on the solution of some of the most important problems in mathematics and the sciences. At the end of June 1993, a large Conference in Harmonic Analysis was held at the University of Paris-Sud at Orsay to celebrate the prominent role played by Jean-Pierre Kahane and his numerous achievements in this field. The large variety of topics discussed in this meeting, ranging from classical Harmonic Analysis to Probability Theory, reflects the intense mathematical curiosity and the broad mathematical interest of Jean-Pierre Kahane. Indeed, all of them are connected to his work. The mornings were devoted to plenary addresses while up to four parallel sessions took place in the afternoons. Altogether, there were about eighty speakers. This wide range of subjects appears in these proceedings which include thirty six articles.