Conformal Geometry And Quasiregular Mappings

Author : Matti Vuorinen
Publisher : Springer
Page : 228 pages
File Size : 40,9 Mb
Release : 2006-11-15
Category : Mathematics
ISBN : 9783540392071

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Conformal Geometry and Quasiregular Mappings by Matti Vuorinen Pdf

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.

Author : Ravi S. Kulkarni
Publisher : Springer-Verlag
Page : 245 pages
File Size : 45,5 Mb
Release : 2013-03-09
Category : Mathematics
ISBN : 9783322906168

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Conformal Geometry by Ravi S. Kulkarni Pdf

Author : Matti Vuorinen
Publisher : Springer
Page : 156 pages
File Size : 40,5 Mb
Release : 2006-11-14
Category : Mathematics
ISBN : 9783540470618

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Quasiconformal Space Mappings by Matti Vuorinen Pdf

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.

Author : Seppo Rickman
Publisher : Springer Science & Business Media
Page : 221 pages
File Size : 47,9 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9783642782015

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Quasiregular Mappings by Seppo Rickman Pdf

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.

Author : Steven G. Krantz
Publisher : Courier Dover Publications
Page : 304 pages
File Size : 40,6 Mb
Release : 2016-03-17
Category : Mathematics
ISBN : 9780486810324

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The Theory and Practice of Conformal Geometry by Steven G. Krantz Pdf

In this original text, prolific mathematics author Steven G. Krantz addresses conformal geometry, a subject that has occupied him for four decades and for which he helped to develop some of the modern theory. This book takes readers with a basic grounding in complex variable theory to the forefront of some of the current approaches to the topic. "Along the way," the author notes in his Preface, "the reader will be exposed to some beautiful function theory and also some of the rudiments of geometry and analysis that make this subject so vibrant and lively." More up-to-date and accessible to advanced undergraduates than most of the other books available in this specific field, the treatment discusses the history of this active and popular branch of mathematics as well as recent developments. Topics include the Riemann mapping theorem, invariant metrics, normal families, automorphism groups, the Schwarz lemma, harmonic measure, extremal length, analytic capacity, and invariant geometry. A helpful Bibliography and Index complete the text.

Author : Dmitry Beliaev
Publisher : World Scientific
Page : 240 pages
File Size : 53,6 Mb
Release : 2019-11-19
Category : Mathematics
ISBN : 9781786346155

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Conformal Maps And Geometry by Dmitry Beliaev Pdf

'I very much enjoyed reading this book … Each chapter comes with well thought-out exercises, solutions to which are given at the end of the chapter. Conformal Maps and Geometry presents key topics in geometric function theory and the theory of univalent functions, and also prepares the reader to progress to study the SLE. It succeeds admirably on both counts.'MathSciNetGeometric function theory is one of the most interesting parts of complex analysis, an area that has become increasingly relevant as a key feature in the theory of Schramm-Loewner evolution.Though Riemann mapping theorem is frequently explored, there are few texts that discuss general theory of univalent maps, conformal invariants, and Loewner evolution. This textbook provides an accessible foundation of the theory of conformal maps and their connections with geometry.It offers a unique view of the field, as it is one of the first to discuss general theory of univalent maps at a graduate level, while introducing more complex theories of conformal invariants and extremal lengths. Conformal Maps and Geometry is an ideal resource for graduate courses in Complex Analysis or as an analytic prerequisite to study the theory of Schramm-Loewner evolution.

Author : Parisa Hariri,Riku Klén,Matti Vuorinen
Publisher : Springer Nature
Page : 504 pages
File Size : 55,7 Mb
Release : 2020-04-11
Category : Mathematics
ISBN : 9783030320683

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Conformally Invariant Metrics and Quasiconformal Mappings by Parisa Hariri,Riku Klén,Matti Vuorinen Pdf

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.

Author : Xianfeng David Gu,Shing-Tung Yau
Publisher : Unknown
Page : 324 pages
File Size : 43,8 Mb
Release : 2008
Category : CD-ROMs
ISBN : UOM:39015080827697

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Computational Conformal Geometry by Xianfeng David Gu,Shing-Tung Yau Pdf

Author : Saminathan Ponnusamy,T. Sugawa,Matti Vuorinen
Publisher : Unknown
Page : 378 pages
File Size : 47,9 Mb
Release : 2007
Category : Mathematics
ISBN : PSU:000061002678

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Quasiconformal Mappings and Their Applications by Saminathan Ponnusamy,T. Sugawa,Matti Vuorinen Pdf

"Quasiconformal Mappings and their Applications covers conformal invariance and conformally invariant metrics, hyperbolic-type metrics and hyperbolic geodesics, isometries of relative metrics, uniform spaces and Gromov hyperbolicity, quasiregular mappings and quasiconformal mappings in n-space, universal Teichmuller space and related topics, quasiminimizers and potential theory, and numerical conformal mapping and circle packings."--BOOK JACKET.

Author : Yunping Jiang,Sudeb Mitra
Publisher : American Mathematical Soc.
Page : 386 pages
File Size : 49,9 Mb
Release : 2012
Category : Mathematics
ISBN : 9780821853405

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Quasiconformal Mappings, Riemann Surfaces, and Teichmuller Spaces by Yunping Jiang,Sudeb Mitra Pdf

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.

Author : Matti Vuorinen
Publisher : Springer
Page : 164 pages
File Size : 41,8 Mb
Release : 1992-05-06
Category : Mathematics
ISBN : 3540554181

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Quasiconformal Space Mappings by Matti Vuorinen Pdf

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.

Author : Francis E. Burstall,Dirk Ferus,Katrin Leschke,Franz Pedit,Ulrich Pinkall
Publisher : Springer
Page : 96 pages
File Size : 48,6 Mb
Release : 2004-10-20
Category : Mathematics
ISBN : 9783540453017

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Conformal Geometry of Surfaces in S4 and Quaternions by Francis E. Burstall,Dirk Ferus,Katrin Leschke,Franz Pedit,Ulrich Pinkall Pdf

The conformal geometry of surfaces recently developed by the authors leads to a unified understanding of algebraic curve theory and the geometry of surfaces on the basis of a quaternionic-valued function theory. The book offers an elementary introduction to the subject but takes the reader to rather advanced topics. Willmore surfaces in the foursphere, their Bäcklund and Darboux transforms are covered, and a new proof of the classification of Willmore spheres is given.

Author : Kari Astala,Tadeusz Iwaniec,Gaven Martin
Publisher : Princeton University Press
Page : 708 pages
File Size : 51,6 Mb
Release : 2009-01-18
Category : Mathematics
ISBN : 0691137773

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Elliptic Partial Differential Equations and Quasiconformal Mappings in the Plane (PMS-48) by Kari Astala,Tadeusz Iwaniec,Gaven Martin Pdf

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.

Author : S. Rickman
Publisher : Springer Verlag
Page : 213 pages
File Size : 52,9 Mb
Release : 1993
Category : Mathematics
ISBN : 0387566481

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Quasiregular Mappings by S. Rickman Pdf

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.

Author : David E. Blair
Publisher : American Mathematical Soc.
Page : 130 pages
File Size : 53,7 Mb
Release : 2000-08-17
Category : Mathematics
ISBN : 9780821826362

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Inversion Theory and Conformal Mapping by David E. Blair Pdf

It is rarely taught in an undergraduate or even graduate curriculum that the only conformal maps in Euclidean space of dimension greater than two are those generated by similarities and inversions in spheres. This is in stark contrast to the wealth of conformal maps in the plane. The principal aim of this text is to give a treatment of this paucity of conformal maps in higher dimensions. The exposition includes both an analytic proof in general dimension and a differential-geometric proof in dimension three. For completeness, enough complex analysis is developed to prove the abundance of conformal maps in the plane. In addition, the book develops inversion theory as a subject, along with the auxiliary theme of circle-preserving maps. A particular feature is the inclusion of a paper by Caratheodory with the remarkable result that any circle-preserving transformation is necessarily a Mobius transformation, not even the continuity of the transformation is assumed. The text is at the level of advanced undergraduates and is suitable for a capstone course, topics course, senior seminar or independent study. Students and readers with university courses in differential geometry or complex analysis bring with them background to build on, but such courses are not essential prerequisites.