Quasiconformal Mappings in the Plane

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Publisher : Springer
ISBN 13 : 9783642655159
Total Pages : 0 pages
Book Rating : 4.6/5 (551 download)

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Book Synopsis Quasiconformal Mappings in the Plane by : Olli Lehto

Download or read book Quasiconformal Mappings in the Plane written by Olli Lehto and published by Springer. This book was released on 2011-11-11 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: The present text is a fairly direct translation of the German edition "Quasikonforme Abbildungen" published in 1965. During the past decade the theory of quasi conformal mappings in the plane has remained relatively stable. We felt, therefore, that major changes were not necessarily required in the text. In view of the recent progress in the higher-dimensional theory we found it preferable to indicate the two-dimensional case in the title. Our sincere thanks are due to K. W. Lucas, who did the major part of the translation work. In shaping the final form of the text with him we received many valuable suggestions from A. J. Lohwater. We are indebted to Anja Aaltonen and Pentti Dyyster for the prepara­ tion of the manuscript, and to Timo Erkama and Tuomas Sorvali for the careful reading and correction of the proofs. Finally, we should like to express our thanks to Springer-Verlag for their friendly coopera­ tion in the production of this volume.

Quasiconformal Mappings in the Plane

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Publisher : Springer
ISBN 13 : 3540394648
Total Pages : 185 pages
Book Rating : 4.5/5 (43 download)

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Book Synopsis Quasiconformal Mappings in the Plane by : J. Krzyz

Download or read book Quasiconformal Mappings in the Plane written by J. Krzyz and published by Springer. This book was released on 2006-11-15 with total page 185 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Elliptic Partial Differential Equations and Quasiconformal Mappings in the Plane

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Publisher : Princeton University Press
ISBN 13 : 1400830117
Total Pages : 696 pages
Book Rating : 4.4/5 (8 download)

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Book Synopsis Elliptic Partial Differential Equations and Quasiconformal Mappings in the Plane by : Kari Astala

Download or read book Elliptic Partial Differential Equations and Quasiconformal Mappings in the Plane written by Kari Astala and published by Princeton University Press. This book was released on 2008-12-29 with total page 696 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book explores the most recent developments in the theory of planar quasiconformal mappings with a particular focus on the interactions with partial differential equations and nonlinear analysis. It gives a thorough and modern approach to the classical theory and presents important and compelling applications across a spectrum of mathematics: dynamical systems, singular integral operators, inverse problems, the geometry of mappings, and the calculus of variations. It also gives an account of recent advances in harmonic analysis and their applications in the geometric theory of mappings. The book explains that the existence, regularity, and singular set structures for second-order divergence-type equations--the most important class of PDEs in applications--are determined by the mathematics underpinning the geometry, structure, and dimension of fractal sets; moduli spaces of Riemann surfaces; and conformal dynamical systems. These topics are inextricably linked by the theory of quasiconformal mappings. Further, the interplay between them allows the authors to extend classical results to more general settings for wider applicability, providing new and often optimal answers to questions of existence, regularity, and geometric properties of solutions to nonlinear systems in both elliptic and degenerate elliptic settings.

Lectures on Quasiconformal Mappings

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Publisher : American Mathematical Soc.
ISBN 13 : 0821836447
Total Pages : 178 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Lectures on Quasiconformal Mappings by : Lars Valerian Ahlfors

Download or read book Lectures on Quasiconformal Mappings written by Lars Valerian Ahlfors and published by American Mathematical Soc.. This book was released on 2006-07-14 with total page 178 pages. Available in PDF, EPUB and Kindle. Book excerpt: Lars Ahlfors's Lectures on Quasiconformal Mappings, based on a course he gave at Harvard University in the spring term of 1964, was first published in 1966 and was soon recognized as the classic it was shortly destined to become. These lectures develop the theory of quasiconformal mappings from scratch, give a self-contained treatment of the Beltrami equation, and cover the basic properties of Teichmuller spaces, including the Bers embedding and the Teichmuller curve. It is remarkable how Ahlfors goes straight to the heart of the matter, presenting major results with a minimum set of prerequisites. Many graduate students and other mathematicians have learned the foundations of the theories of quasiconformal mappings and Teichmuller spaces from these lecture notes. This edition includes three new chapters. The first, written by Earle and Kra, describes further developments in the theory of Teichmuller spaces and provides many references to the vast literature on Teichmuller spaces and quasiconformal mappings. The second, by Shishikura, describes how quasiconformal mappings have revitalized the subject of complex dynamics. The third, by Hubbard, illustrates the role of these mappings in Thurston's theory of hyperbolic structures on 3-manifolds. Together, these three new chapters exhibit the continuing vitality and importance of the theory of quasiconformal mappings.

Harmonic Quasiconformal Mappings and Hyperbolic Type Metrics

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Publisher : Springer
ISBN 13 : 9783030225933
Total Pages : 163 pages
Book Rating : 4.2/5 (259 download)

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Book Synopsis Harmonic Quasiconformal Mappings and Hyperbolic Type Metrics by : Vesna Todorčević

Download or read book Harmonic Quasiconformal Mappings and Hyperbolic Type Metrics written by Vesna Todorčević and published by Springer. This book was released on 2020-08-15 with total page 163 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book presents a research area in geometric function theory concerned with harmonic quasiconformal mappings and hyperbolic type metrics defined on planar and multidimensional domains. The classes of quasiconformal and quasiregular mappings are well established areas of study in this field as these classes are natural and fruitful generalizations of the class of analytic functions in the planar case. The book contains many concrete examples, as well as detailed proofs and explanations of motivations behind given results, gradually bringing the reader to the forefront of current research in the area. This monograph was written for a wide readership from graduate students of mathematical analysis to researchers working in this or related areas of mathematics who want to learn the tools or work on open problems listed in various parts of the book.

Quasiconformal Mappings and Analysis

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Publisher : Springer Science & Business Media
ISBN 13 : 1461206057
Total Pages : 379 pages
Book Rating : 4.4/5 (612 download)

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Book Synopsis Quasiconformal Mappings and Analysis by : Peter Duren

Download or read book Quasiconformal Mappings and Analysis written by Peter Duren and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 379 pages. Available in PDF, EPUB and Kindle. Book excerpt: In honor of Frederick W. Gehring on the occasion of his 70th birthday, an international conference on ""Quasiconformal mappings and analysis"" was held in Ann Arbor in August 1995. The 9 main speakers of the conference (Astala, Earle, Jones, Kra, Lehto, Martin, Pommerenke, Sullivan, and Vaisala) provide broad expository articles on various aspects of quasiconformal mappings and their relations to other areas of analysis. 12 other distinguished mathematicians contribute articles to this volume.

Harmonic Mappings in the Plane

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Publisher : Cambridge University Press
ISBN 13 : 9781139451277
Total Pages : 236 pages
Book Rating : 4.4/5 (512 download)

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Book Synopsis Harmonic Mappings in the Plane by : Peter Duren

Download or read book Harmonic Mappings in the Plane written by Peter Duren and published by Cambridge University Press. This book was released on 2004-03-29 with total page 236 pages. Available in PDF, EPUB and Kindle. Book excerpt: Harmonic mappings in the plane are univalent complex-valued harmonic functions of a complex variable. Conformal mappings are a special case where the real and imaginary parts are conjugate harmonic functions, satisfying the Cauchy-Riemann equations. Harmonic mappings were studied classically by differential geometers because they provide isothermal (or conformal) parameters for minimal surfaces. More recently they have been actively investigated by complex analysts as generalizations of univalent analytic functions, or conformal mappings. Many classical results of geometric function theory extend to harmonic mappings, but basic questions remain unresolved. This book is the first comprehensive account of the theory of planar harmonic mappings, treating both the generalizations of univalent analytic functions and the connections with minimal surfaces. Essentially self-contained, the book contains background material in complex analysis and a full development of the classical theory of minimal surfaces, including the Weierstrass-Enneper representation. It is designed to introduce non-specialists to a beautiful area of complex analysis and geometry.

Quasiconformal Surgery in Holomorphic Dynamics

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Publisher : Cambridge University Press
ISBN 13 : 1107042917
Total Pages : 433 pages
Book Rating : 4.1/5 (7 download)

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Book Synopsis Quasiconformal Surgery in Holomorphic Dynamics by : Bodil Branner

Download or read book Quasiconformal Surgery in Holomorphic Dynamics written by Bodil Branner and published by Cambridge University Press. This book was released on 2014-01-23 with total page 433 pages. Available in PDF, EPUB and Kindle. Book excerpt: A comprehensive introduction to quasiconformal surgery in holomorphic dynamics. Contains a wide variety of applications and illustrations.

Quasiconformal Mappings and Sobolev Spaces

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Publisher : Springer Science & Business Media
ISBN 13 : 9400919220
Total Pages : 389 pages
Book Rating : 4.4/5 (9 download)

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Book Synopsis Quasiconformal Mappings and Sobolev Spaces by : V.M. Gol'dshtein

Download or read book Quasiconformal Mappings and Sobolev Spaces written by V.M. Gol'dshtein and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 389 pages. Available in PDF, EPUB and Kindle. Book excerpt: 'Ht moi ..., si j'avait su comment en revenir, One lemce mathematics has rendered the je n'y serai. point aile.' human race. It has put common sense back Jule. Verne ... "'" it belong., on the topmost shelf next to the dusty caniller labelled 'discarded non- The series is divergent; therefore we may be sense'. able to do something with it. Eric T. Bell O. Heaviside Mathematics is a tool for thought. A highly necessary tool in a world where both feedback and non linearities abound. Similarly, all kinds of parts of mathematics serve as tools for other parts and for other sciences. Applying a simple rewriting rule to the quote on the right above one finds such statements as: 'One service topology has rendered mathematical physics .. .'; 'One service logic has rendered com puter science .. .'; 'One service category theory has rendered mathematics .. .'. All arguably true. And all statements obtainable this way form part of the raison d'~re of this series

Quasiregular Mappings

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Publisher : Springer Science & Business Media
ISBN 13 : 3642782019
Total Pages : 221 pages
Book Rating : 4.6/5 (427 download)

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Book Synopsis Quasiregular Mappings by : Seppo Rickman

Download or read book Quasiregular Mappings written by Seppo Rickman and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 221 pages. Available in PDF, EPUB and Kindle. Book excerpt: Quasiregular Mappings extend quasiconformal theory to the noninjective case.They give a natural and beautiful generalization of the geometric aspects ofthe theory of analytic functions of one complex variable to Euclidean n-space or, more generally, to Riemannian n-manifolds. This book is a self-contained exposition of the subject. A braod spectrum of results of both analytic and geometric character are presented, and the methods vary accordingly. The main tools are the variational integral method and the extremal length method, both of which are thoroughly developed here. Reshetnyak's basic theorem on discreteness and openness is used from the beginning, but the proof by means of variational integrals is postponed until near the end. Thus, the method of extremal length is being used at an early stage and leads, among other things, to geometric proofs of Picard-type theorems and a defect relation, which are some of the high points of the present book.

Quasiconformal Mappings, Riemann Surfaces, and Teichmuller Spaces

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Publisher : American Mathematical Soc.
ISBN 13 : 0821853406
Total Pages : 386 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Quasiconformal Mappings, Riemann Surfaces, and Teichmuller Spaces by : Yunping Jiang

Download or read book Quasiconformal Mappings, Riemann Surfaces, and Teichmuller Spaces written by Yunping Jiang and published by American Mathematical Soc.. This book was released on 2012 with total page 386 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

A Primer on Mapping Class Groups

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Publisher : Princeton University Press
ISBN 13 : 0691147949
Total Pages : 490 pages
Book Rating : 4.6/5 (911 download)

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Book Synopsis A Primer on Mapping Class Groups by : Benson Farb

Download or read book A Primer on Mapping Class Groups written by Benson Farb and published by Princeton University Press. This book was released on 2012 with total page 490 pages. Available in PDF, EPUB and Kindle. Book excerpt: The study of the mapping class group Mod(S) is a classical topic that is experiencing a renaissance. It lies at the juncture of geometry, topology, and group theory. This book explains as many important theorems, examples, and techniques as possible, quickly and directly, while at the same time giving full details and keeping the text nearly self-contained. The book is suitable for graduate students. A Primer on Mapping Class Groups begins by explaining the main group-theoretical properties of Mod(S), from finite generation by Dehn twists and low-dimensional homology to the Dehn-Nielsen-Baer theorem. Along the way, central objects and tools are introduced, such as the Birman exact sequence, the complex of curves, the braid group, the symplectic representation, and the Torelli group. The book then introduces Teichmüller space and its geometry, and uses the action of Mod(S) on it to prove the Nielsen-Thurston classification of surface homeomorphisms. Topics include the topology of the moduli space of Riemann surfaces, the connection with surface bundles, pseudo-Anosov theory, and Thurston's approach to the classification.

Complex Dynamics and Renormalization

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Publisher : Princeton University Press
ISBN 13 : 9780691029818
Total Pages : 228 pages
Book Rating : 4.0/5 (298 download)

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Book Synopsis Complex Dynamics and Renormalization by : Curtis T. McMullen

Download or read book Complex Dynamics and Renormalization written by Curtis T. McMullen and published by Princeton University Press. This book was released on 1994-12-19 with total page 228 pages. Available in PDF, EPUB and Kindle. Book excerpt: Addressing researchers and graduate students in the active meeting ground of analysis, geometry, and dynamics, this book presents a study of renormalization of quadratic polynomials and a rapid introduction to techniques in complex dynamics. Its central concern is the structure of an infinitely renormalizable quadratic polynomial f(z) = z2 + c. As discovered by Feigenbaum, such a mapping exhibits a repetition of form at infinitely many scales. Drawing on universal estimates in hyperbolic geometry, this work gives an analysis of the limiting forms that can occur and develops a rigidity criterion for the polynomial f. This criterion supports general conjectures about the behavior of rational maps and the structure of the Mandelbrot set. The course of the main argument entails many facets of modern complex dynamics. Included are foundational results in geometric function theory, quasiconformal mappings, and hyperbolic geometry. Most of the tools are discussed in the setting of general polynomials and rational maps.

Quasiconformal Maps and Teichmüller Theory

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Publisher : Oxford University Press, USA
ISBN 13 :
Total Pages : 208 pages
Book Rating : 4.F/5 ( download)

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Book Synopsis Quasiconformal Maps and Teichmüller Theory by : Alastair Fletcher

Download or read book Quasiconformal Maps and Teichmüller Theory written by Alastair Fletcher and published by Oxford University Press, USA. This book was released on 2007 with total page 208 pages. Available in PDF, EPUB and Kindle. Book excerpt: Publisher description

Lectures on Quasiconformal Mappings

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Publisher :
ISBN 13 :
Total Pages : 128 pages
Book Rating : 4.3/5 (91 download)

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Book Synopsis Lectures on Quasiconformal Mappings by : Frederick W. Gehring

Download or read book Lectures on Quasiconformal Mappings written by Frederick W. Gehring and published by . This book was released on 1975 with total page 128 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Complex Dynamics

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Publisher : Springer Science & Business Media
ISBN 13 : 1461243645
Total Pages : 181 pages
Book Rating : 4.4/5 (612 download)

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Book Synopsis Complex Dynamics by : Lennart Carleson

Download or read book Complex Dynamics written by Lennart Carleson and published by Springer Science & Business Media. This book was released on 2013-11-11 with total page 181 pages. Available in PDF, EPUB and Kindle. Book excerpt: A discussion of the properties of conformal mappings in the complex plane, closely related to the study of fractals and chaos. Indeed, the book ends in a detailed study of the famous Mandelbrot set, which describes very general properties of such mappings. Focusing on the analytic side of this contemporary subject, the text was developed from a course taught over several semesters and aims to help students and instructors to familiarize themselves with complex dynamics. Topics covered include: conformal and quasi-conformal mappings, fixed points and conjugations, basic rational iteration, classification of periodic components, critical points and expanding maps, some applications of conformal mappings, the local geometry of the Fatou set, and quadratic polynomials and the Mandelbrot set.

Boundary Behaviour of Conformal Maps

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Publisher : Springer Science & Business Media
ISBN 13 : 3662027704
Total Pages : 307 pages
Book Rating : 4.6/5 (62 download)

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Book Synopsis Boundary Behaviour of Conformal Maps by : Christian Pommerenke

Download or read book Boundary Behaviour of Conformal Maps written by Christian Pommerenke and published by Springer Science & Business Media. This book was released on 2013-04-09 with total page 307 pages. Available in PDF, EPUB and Kindle. Book excerpt: We study the boundary behaviour of a conformal map of the unit disk onto an arbitrary simply connected plane domain. A principal aim of the theory is to obtain a one-to-one correspondence between analytic properties of the function and geometrie properties of the domain. In the classical applications of conformal mapping, the domain is bounded by a piecewise smooth curve. In many recent applications however, the domain has a very bad boundary. It may have nowhere a tangent as is the case for Julia sets. Then the conformal map has many unexpected properties, for instance almost all the boundary is mapped onto almost nothing and vice versa. The book is meant for two groups of users. (1) Graduate students and others who, at various levels, want to learn about conformal mapping. Most sections contain exercises to test the understand ing. They tend to be fairly simple and only a few contain new material. Pre requisites are general real and complex analyis including the basic facts about conformal mapping (e.g. AhI66a). (2) Non-experts who want to get an idea of a particular aspect of confor mal mapping in order to find something useful for their work. Most chapters therefore begin with an overview that states some key results avoiding tech nicalities. The book is not meant as an exhaustive survey of conformal mapping. Several important aspects had to be omitted, e.g. numerical methods (see e.g.