Quasiregular Mappings

Author : Seppo Rickman
Publisher : Springer Science & Business Media
Page : 221 pages
File Size : 55,8 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 : Matti Vuorinen
Publisher : Springer
Page : 228 pages
File Size : 52,6 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 : S. Rickman
Publisher : Springer Verlag
Page : 213 pages
File Size : 47,7 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 : Matti Vuorinen
Publisher : Springer
Page : 156 pages
File Size : 48,5 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 : Kari Astala,Tadeusz Iwaniec,Gaven Martin
Publisher : Princeton University Press
Page : 708 pages
File Size : 41,9 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 : Peter Duren,Juha Heinonen,Brad Osgood,Bruce Palka
Publisher : Springer Science & Business Media
Page : 379 pages
File Size : 44,8 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781461206057

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Quasiconformal Mappings and Analysis by Peter Duren,Juha Heinonen,Brad Osgood,Bruce Palka Pdf

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.

Author : Matti Vuorinen
Publisher : Unknown
Page : 550 pages
File Size : 47,9 Mb
Release : 1976
Category : Analytic functions
ISBN : UCSD:31822033760117

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Exceptional Sets and Boundary Behavior of Quasiregular Mappings in N-space by Matti Vuorinen Pdf

Author : Yunping Jiang,Sudeb Mitra
Publisher : American Mathematical Soc.
Page : 386 pages
File Size : 53,8 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 : Jorma Jormakka
Publisher : Unknown
Page : 52 pages
File Size : 44,9 Mb
Release : 1988
Category : Quasiconformal mappings
ISBN : UCSD:31822003136587

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The Existence of Quasiregular Mappings from R3 to Closed Orientable 3-manifolds by Jorma Jormakka Pdf

Author : Stanislav Hencl,Pekka Koskela
Publisher : Springer
Page : 176 pages
File Size : 48,6 Mb
Release : 2014-01-24
Category : Mathematics
ISBN : 9783319031736

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Lectures on Mappings of Finite Distortion by Stanislav Hencl,Pekka Koskela Pdf

In this book we introduce the class of mappings of finite distortion as a generalization of the class of mappings of bounded distortion. Connections with models of nonlinear elasticity are also discussed. We study continuity properties, behavior of our mappings on null sets, topological properties like openness and discreteness, regularity of the potential inverse mappings and many other aspects.

Author : Vesna Todorčević
Publisher : Springer
Page : 163 pages
File Size : 44,5 Mb
Release : 2019-07-24
Category : Mathematics
ISBN : 9783030225919

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Harmonic Quasiconformal Mappings and Hyperbolic Type Metrics by Vesna Todorčević Pdf

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.

Author : Parisa Hariri,Riku Klén,Matti Vuorinen
Publisher : Springer Nature
Page : 504 pages
File Size : 41,5 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 : Boris N. Apanasov
Publisher : Walter de Gruyter GmbH & Co KG
Page : 714 pages
File Size : 46,5 Mb
Release : 2024-07-22
Category : Mathematics
ISBN : 9783110784138

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Dynamics of Discrete Group Action by Boris N. Apanasov Pdf

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.

Author : Cabiria Andreian Cazacu,Olli E Lehto,Themistocles M Rassias
Publisher : World Scientific
Page : 736 pages
File Size : 46,6 Mb
Release : 1998-11-06
Category : Mathematics
ISBN : 9789814498593

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Analysis and Topology by Cabiria Andreian Cazacu,Olli E Lehto,Themistocles M Rassias Pdf

The goal of this book is to investigate further the interdisciplinary interaction between Mathematical Analysis and Topology. It provides an attempt to study various approaches in the topological applications and influence to Function Theory, Calculus of Variations, Functional Analysis and Approximation Theory. The volume is dedicated to the memory of S Stoilow. Contents:Brief Summary of My Research Work (S Stoilow)On Stoilow's Work and Its Influence (C A Cazacu & T M Rassias)Contributions to Stoilow's Theory of Riemann Coverings (C A Cazacu)On the Link of Simultaneous Approximations to Vectorially Minimal Projections (A Bacopoulos)Schwarz Problem for Cauchy-Riemann Systems in Several Complex Variables (H Begehr & A Dzhuraev)Generalized Multivalued Variational Inequalities (H Ben-El-Mechaiekh & G Isac)On the Zorn Spaces in Beurling's Approach to the Riemann Hypothesis (H Bercovici & C Foias)Quasi Bounded Excessive Functions and Revuz Measures (L Beznea & N Boboc)Potential Theory on Ordered Sets (N Boboc & Gh Bucur)Cutting and Gluing Back Along a Closed Simple Curve on a Riemann Surface (D Burghelea & C Constantinescu)About Cases of Equality Between the p-Module and the p-Capacity (P Caraman)Some Examples of Dynamical Systems (K Ciesielski)Applications of Controlled Convergence in Analysis (A Cornea)A Generalization of a Theorem of Weierstrass (M Cristea)Conditions D'existence et Propriétés D'une Métrique Conformément Invariante sur les Variétés Riemanniennes Non Compactes (J Ferrand)Barycentric Subdivisions of Partitions with Applications to Higher Dimensional Symbolic Dynamics and Limit Expansions of Homeomorphisms (B Günther)Ricci Curvature, Harnack Functions, and Picard Type Theorems for Quasiregular Mappings (I Holopainen & S Rickman)On Conformal Weldings which Generate Welding Curves of Finite Rotation (A Huber)The Liouville Theorem (T Iwaniec & G Martin)Pseudocontinuous Functions (R A Johnson & W Wilczy(ski)Local Harmonic Analysis for Domains in Rn of Finite Measure (P E T Jorgensen & S Pedersen)Simion Stoilow and the Romanian Mathematical School (M Jurchescu)The Concept of Global Analytic Function and Riemann Surface in Stoilow's Work (M Jurchescu)Pinched 2-Component Kleinian Groups (I Kra & B Maskit)Quasireflections and Holomorphic Functions (S L Krushkal)Der Konforme Modul von Vierecken (R Kühnau)Stoilow's Work in Real Analysis: Its Significance and Its Impact (S Marcus)The Isomorphism Theorem of Kleinian Groups (K Matsuzaki)Topological Results in Analytic Convexity (N Mihalache)Conditions for Differomorphism in the Complex Plane (P T Mocanu)Parametrization of Teichmüller Space by Length Parameters (T Nakanishi & M Näätänen)A Remark on the Integrability and Boundedness of Automorphic Forms (T Ohsawa)Duality for Multiobjective Fractional Programming Problems Involving n-Set Functions (V Preda)Stability and Set-Valued Functions (T M Rassias)Steiner Symmetrization and the Conformal Moduli of Parallelograms (E Reich)Hilbert's Sixteenth Problem (P X Sheng)Non-Existence of Quasimeromorphic Automorphic Mappings (U Srebro)Certain Conjectures and Theorems Involving the Fractional Derivatives of Analytic and Univalent Functions (H M Srivastava)Extremal Teichmüller Mappings with Given Asymptotic Behaviour (K Strebel)Free Quasiconformality in Banach Spaces IV (J Väisälä)Mapping the Disk to Convex Subregions (J A Velling) Readership: Mathematicians and graduate students in mathematics. keywords:Analysis;Topology;Memorial

Author : Juha Heinonen,Tero Kipelainen,Olli Martio
Publisher : Courier Dover Publications
Page : 417 pages
File Size : 49,6 Mb
Release : 2018-05-16
Category : Mathematics
ISBN : 9780486824253

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Nonlinear Potential Theory of Degenerate Elliptic Equations by Juha Heinonen,Tero Kipelainen,Olli Martio Pdf

A self-contained treatment appropriate for advanced undergraduate and graduate students, this volume offers a detailed development of the necessary background for its survey of the nonlinear potential theory of superharmonic functions. Starting with the theory of weighted Sobolev spaces, the text advances to the theory of weighted variational capacity. Succeeding chapters investigate solutions and supersolutions of equations, with emphasis on refined Sobolev spaces, variational integrals, and harmonic functions. Chapter 7 defines superharmonic functions via the comparison principle, and chapters 8 through 14 form the core of the nonlinear potential theory of superharmonic functions. Topics include balayage; Perron's method, barriers, and resolutivity; polar sets; harmonic measure; fine topology; harmonic morphisms; and quasiregular mappings. The book concludes with explorations of axiomatic nonlinear potential theory and helpful appendixes.