Conformal Geometry And Quasiregular Mappings

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Conformal Geometry and Quasiregular Mappings

Author : Matti Vuorinen
Publisher : Springer
ISBN 13 : 3540392076
Total Pages : 228 pages
Book Rating : 4.5/5 (43 download)

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Book Synopsis Conformal Geometry and Quasiregular Mappings by : Matti Vuorinen

Download or read book Conformal Geometry and Quasiregular Mappings written by Matti Vuorinen and published by Springer. This book was released on 2006-11-15 with total page 228 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is an introduction to the theory of spatial quasiregular mappings intended for the uninitiated reader. At the same time the book also addresses specialists in classical analysis and, in particular, geometric function theory. The text leads the reader to the frontier of current research and covers some most recent developments in the subject, previously scatterd through the literature. A major role in this monograph is played by certain conformal invariants which are solutions of extremal problems related to extremal lengths of curve families. These invariants are then applied to prove sharp distortion theorems for quasiregular mappings. One of these extremal problems of conformal geometry generalizes a classical two-dimensional problem of O. Teichmüller. The novel feature of the exposition is the way in which conformal invariants are applied and the sharp results obtained should be of considerable interest even in the two-dimensional particular case. This book combines the features of a textbook and of a research monograph: it is the first introduction to the subject available in English, contains nearly a hundred exercises, a survey of the subject as well as an extensive bibliography and, finally, a list of open problems.

Conformal Geometry of Discrete Groups and Manifolds

Author : Boris N. Apanasov
Publisher : Walter de Gruyter
ISBN 13 : 3110808056
Total Pages : 541 pages
Book Rating : 4.1/5 (18 download)

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Book Synopsis Conformal Geometry of Discrete Groups and Manifolds by : Boris N. Apanasov

Download or read book Conformal Geometry of Discrete Groups and Manifolds written by Boris N. Apanasov and published by Walter de Gruyter. This book was released on 2011-06-24 with total page 541 pages. Available in PDF, EPUB and Kindle. Book excerpt: The aim of the Expositions is to present new and important developments in pure and applied mathematics. Well established in the community over more than two decades, the series offers a large library of mathematical works, including several important classics. The volumes supply thorough and detailed expositions of the methods and ideas essential to the topics in question. In addition, they convey their relationships to other parts of mathematics. The series is addressed to advanced readers interested in a thorough study of the subject. Editorial Board Lev Birbrair, Universidade Federal do Ceará, Fortaleza, Brasil Walter D. Neumann, Columbia University, New York, USA Markus J. Pflaum, University of Colorado, Boulder, USA Dierk Schleicher, Jacobs University, Bremen, Germany Katrin Wendland, University of Freiburg, Germany Honorary Editor Victor P. Maslov, Russian Academy of Sciences, Moscow, Russia Titles in planning include Yuri A. Bahturin, Identical Relations in Lie Algebras (2019) Yakov G. Berkovich, Lev G. Kazarin, and Emmanuel M. Zhmud', Characters of Finite Groups, Volume 2 (2019) Jorge Herbert Soares de Lira, Variational Problems for Hypersurfaces in Riemannian Manifolds (2019) Volker Mayer, Mariusz Urbański, and Anna Zdunik, Random and Conformal Dynamical Systems (2021) Ioannis Diamantis, Boštjan Gabrovšek, Sofia Lambropoulou, and Maciej Mroczkowski, Knot Theory of Lens Spaces (2021)

Quasiconformal Mappings and Analysis

Author : Peter Duren
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.

Conformally Invariant Metrics and Quasiconformal Mappings

Author : Parisa Hariri
Publisher : Springer Nature
ISBN 13 : 3030320685
Total Pages : 504 pages
Book Rating : 4.0/5 (33 download)

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Book Synopsis Conformally Invariant Metrics and Quasiconformal Mappings by : Parisa Hariri

Download or read book Conformally Invariant Metrics and Quasiconformal Mappings written by Parisa Hariri and published by Springer Nature. This book was released on 2020-04-11 with total page 504 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is an introduction to the theory of quasiconformal and quasiregular mappings in the euclidean n-dimensional space, (where n is greater than 2). There are many ways to develop this theory as the literature shows. The authors' approach is based on the use of metrics, in particular conformally invariant metrics, which will have a key role throughout the whole book. The intended readership consists of mathematicians from beginning graduate students to researchers. The prerequisite requirements are modest: only some familiarity with basic ideas of real and complex analysis is expected.

Elliptic Partial Differential Equations and Quasiconformal Mappings in the Plane

Author : Kari Astala
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.

Quasiconformal Space Mappings

Author : Matti Vuorinen
Publisher : Springer
ISBN 13 : 3540470611
Total Pages : 156 pages
Book Rating : 4.5/5 (44 download)

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Book Synopsis Quasiconformal Space Mappings by : Matti Vuorinen

Download or read book Quasiconformal Space Mappings written by Matti Vuorinen and published by Springer. This book was released on 2006-11-14 with total page 156 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume is a collection of surveys on function theory in euclidean n-dimensional spaces centered around the theme of quasiconformal space mappings. These surveys cover or are related to several topics including inequalities for conformal invariants and extremal length, distortion theorems, L(p)-theory of quasiconformal maps, nonlinear potential theory, variational calculus, value distribution theory of quasiregular maps, topological properties of discrete open mappings, the action of quasiconformal maps in special classes of domains, and global injectivity theorems. The present volume is the first collection of surveys on Quasiconformal Space Mappings since the origin of the theory in 1960 and this collection provides in compact form access to a wide spectrum of recent results due to well-known specialists. CONTENTS: G.D. Anderson, M.K. Vamanamurthy, M. Vuorinen: Conformal invariants, quasiconformal maps and special functions.- F.W. Gehring: Topics in quasiconformal mappings.- T.Iwaniec: L(p)-theory of quasiregular mappings.- O. Martio: Partial differential equations and quasiregular mappings.- Yu.G. Reshetnyak: On functional classes invariant relative to homothetics.- S. Rickman: Picard's theorem and defect relation for quasiconformal mappings.- U. Srebro: Topological properties of quasiregular mappings.- J. V{is{l{: Domains and maps.- V.A. Zorich: The global homeomorphism theorem for space quasiconformal mappings, its development and related open problems.

Quasiregular Mappings

Author : Seppo Rickman
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

Author : Yunping Jiang
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.

Conformal Geometry

Author : Ravi S. Kulkarni
Publisher : Vieweg+teubner Verlag
ISBN 13 :
Total Pages : 256 pages
Book Rating : 4.3/5 (91 download)

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Book Synopsis Conformal Geometry by : Ravi S. Kulkarni

Download or read book Conformal Geometry written by Ravi S. Kulkarni and published by Vieweg+teubner Verlag. This book was released on 1988 with total page 256 pages. Available in PDF, EPUB and Kindle. Book excerpt: The contributions in this volume summarize parts of a seminar on conformal geometry which was held at the Max-Planck-Institut fur Mathematik in Bonn during the academic year 1985/86. The intention of this seminar was to study conformal structures on mani folds from various viewpoints. The motivation to publish seminar notes grew out of the fact that in spite of the basic importance of this field to many topics of current interest (low-dimensional topology, analysis on manifolds . . . ) there seems to be no coherent introduction to conformal geometry in the literature. We have tried to make the material presented in this book self-contained, so it should be accessible to students with some background in differential geometry. Moreover, we hope that it will be useful as a reference and as a source of inspiration for further research. Ravi Kulkarni/Ulrich Pinkall Conformal Structures and Mobius Structures Ravi S. Kulkarni* Contents § 0 Introduction 2 § 1 Conformal Structures 4 § 2 Conformal Change of a Metric, Mobius Structures 8 § 3 Liouville's Theorem 12 n §4 The GroupsM(n) andM(E ) 13 § 5 Connection with Hyperbol ic Geometry 16 § 6 Constructions of Mobius Manifolds 21 § 7 Development and Holonomy 31 § 8 Ideal Boundary, Classification of Mobius Structures 35 * Partially supported by the Max-Planck-Institut fur Mathematik, Bonn, and an NSF grant. 2 §O Introduction (0. 1) Historically, the stereographic projection and the Mercator projection must have appeared to mathematicians very startling.

Moduli in Modern Mapping Theory

Author : Olli Martio
Publisher : Springer Science & Business Media
ISBN 13 : 0387855882
Total Pages : 368 pages
Book Rating : 4.3/5 (878 download)

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Book Synopsis Moduli in Modern Mapping Theory by : Olli Martio

Download or read book Moduli in Modern Mapping Theory written by Olli Martio and published by Springer Science & Business Media. This book was released on 2008-11-09 with total page 368 pages. Available in PDF, EPUB and Kindle. Book excerpt: Based on recent research papers, this book presents a modern account of mapping theory with emphasis on quasiconformal mapping and its generalizations. It contains an extensive bibliography.

Geometric Function Theory and Non-linear Analysis

Author : Tadeusz Iwaniec
Publisher : Clarendon Press
ISBN 13 : 9780198509295
Total Pages : 576 pages
Book Rating : 4.5/5 (92 download)

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Book Synopsis Geometric Function Theory and Non-linear Analysis by : Tadeusz Iwaniec

Download or read book Geometric Function Theory and Non-linear Analysis written by Tadeusz Iwaniec and published by Clarendon Press. This book was released on 2001 with total page 576 pages. Available in PDF, EPUB and Kindle. Book excerpt: Iwaniec (math, Syracuse U.) and Martin (math, U. of Auckland) explain recent developments in the geometry of mappings, related to functions or deformations between subsets of the Euclidean n-space Rn and more generally between manifolds or other geometric objects. Material on mappings intersects with aspects of differential geometry, topology, partial differential equations, harmonic analysis, and the calculus of variations. Chapters cover topics such as conformal mappings, stability of the Mobius group, Sobolev theory and function spaces, the Liouville theorem, even dimensions, Picard and Montel theorems in space, uniformly quasiregular mappings, and quasiconformal groups. c. Book News Inc.

Current Topics in Analytic Function Theory

Author : H. M. Srivastava
Publisher : World Scientific
ISBN 13 : 9789810209322
Total Pages : 480 pages
Book Rating : 4.2/5 (93 download)

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Book Synopsis Current Topics in Analytic Function Theory by : H. M. Srivastava

Download or read book Current Topics in Analytic Function Theory written by H. M. Srivastava and published by World Scientific. This book was released on 1992 with total page 480 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume is a collection of research-and-survey articles by eminent and active workers around the world on the various areas of current research in the theory of analytic functions.Many of these articles emerged essentially from the proceedings of, and various deliberations at, three recent conferences in Japan and Korea: An International Seminar on Current Topics in Univalent Functions and Their Applications which was held in August 1990, in conjunction with the International Congress of Mathematicians at Kyoto, at Kinki University in Osaka; An International Seminar on Univalent Functions, Fractional Calculus, and Their Applications which was held in October 1990 at Fukuoka University; and also the Japan-Korea Symposium on Univalent Functions which was held in January 1991 at Gyeongsang National University in Chinju.

The Beltrami Equation

Author : Vladimir Gutlyanskii
Publisher : Springer Science & Business Media
ISBN 13 : 1461431913
Total Pages : 309 pages
Book Rating : 4.4/5 (614 download)

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Book Synopsis The Beltrami Equation by : Vladimir Gutlyanskii

Download or read book The Beltrami Equation written by Vladimir Gutlyanskii and published by Springer Science & Business Media. This book was released on 2012-04-23 with total page 309 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is devoted to the Beltrami equations that play a significant role in Geometry, Analysis and Physics and, in particular, in the study of quasiconformal mappings and their generalizations, Riemann surfaces, Kleinian groups, Teichmuller spaces, Clifford analysis, meromorphic functions, low dimensional topology, holomorphic motions, complex dynamics, potential theory, electrostatics, magnetostatics, hydrodynamics and magneto-hydrodynamics. The purpose of this book is to present the recent developments in the theory of Beltrami equations; especially those concerning degenerate and alternating Beltrami equations. The authors study a wide circle of problems like convergence, existence, uniqueness, representation, removal of singularities, local distortion estimates and boundary behavior of solutions to the Beltrami equations. The monograph contains a number of new types of criteria in the given problems, particularly new integral conditions for the existence of regular solutions to the Beltrami equations that turned out to be not only sufficient but also necessary. The most important feature of this book concerns the unified geometric approach based on the modulus method that is effectively applied to solving the mentioned problems. Moreover, it is characteristic for the book application of many new concepts as strong ring solutions, tangent dilatations, weakly flat and strongly accessible boundaries, functions of finite mean oscillations and new integral conditions that make possible to realize a more deep and refined analysis of problems related to the Beltrami equations. Mastering and using these new tools also gives essential advantages for the reader in the research of modern problems in many other domains. Every mathematics graduate library should have a copy of this book.

Computational Methods And Function Theory 1997 - Proceedings Of The Third Cmft Conference

Author : Nicolas Papamichael
Publisher : World Scientific
ISBN 13 : 9814544396
Total Pages : 666 pages
Book Rating : 4.8/5 (145 download)

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Book Synopsis Computational Methods And Function Theory 1997 - Proceedings Of The Third Cmft Conference by : Nicolas Papamichael

Download or read book Computational Methods And Function Theory 1997 - Proceedings Of The Third Cmft Conference written by Nicolas Papamichael and published by World Scientific. This book was released on 1999-04-14 with total page 666 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains refereed state-of-the-art research articles and extensive surveys on the various aspects of interaction of complex variables and scientific computation as well as on related areas such as function theory and approximation theory.

Dynamics of Discrete Group Action

Author : Boris N. Apanasov
Publisher : Walter de Gruyter GmbH & Co KG
ISBN 13 : 3110784130
Total Pages : 714 pages
Book Rating : 4.1/5 (17 download)

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Book Synopsis Dynamics of Discrete Group Action by : Boris N. Apanasov

Download or read book Dynamics of Discrete Group Action written by Boris N. Apanasov and published by Walter de Gruyter GmbH & Co KG. This book was released on 2024-07-22 with total page 714 pages. Available in PDF, EPUB and Kindle. Book excerpt: Provides the first systematic study of geometry and topology of locally symmetric rank one manifolds and dynamics of discrete action of their fundamental groups. In addition to geometry and topology, this study involves several other areas of Mathematics – from algebra of varieties of groups representations and geometric group theory, to geometric analysis including classical questions from function theory.

Linear and Complex Analysis Problem Book 3

Author : Victor P. Havin
Publisher : Springer
ISBN 13 : 3540483683
Total Pages : 529 pages
Book Rating : 4.5/5 (44 download)

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Book Synopsis Linear and Complex Analysis Problem Book 3 by : Victor P. Havin

Download or read book Linear and Complex Analysis Problem Book 3 written by Victor P. Havin and published by Springer. This book was released on 2006-12-08 with total page 529 pages. Available in PDF, EPUB and Kindle. Book excerpt: The 2-volume-book is an updated, reorganized and considerably enlarged version of the previous edition of the Research Problem Book in Analysis (LNM 1043), a collection familiar to many analysts, that has sparked off much research. This new edition, created in a joint effort by a large team of analysts, is, like its predecessor, a collection of unsolved problems of modern analysis designed as informally written mini-articles, each containing not only a statement of a problem but also historical and metho- dological comments, motivation, conjectures and discussion of possible connections, of plausible approaches as well as a list of references. There are now 342 of these mini- articles, almost twice as many as in the previous edition, despite the fact that a good deal of them have been solved!

Harmonic Quasiconformal Mappings and Hyperbolic Type Metrics

Author : Vesna Todorčević
Publisher : Springer
ISBN 13 : 3030225917
Total Pages : 176 pages
Book Rating : 4.0/5 (32 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 2019-07-24 with total page 176 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.