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Space Mappings With Bounded Distortion
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Book Synopsis Space Mappings with Bounded Distortion by : I_Uri_ Grigor_evich Reshetni_ak
Download or read book Space Mappings with Bounded Distortion written by I_Uri_ Grigor_evich Reshetni_ak and published by American Mathematical Soc.. This book was released on 1989-12-31 with total page 384 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is intended for researchers and students concerned with questions in analysis and function theory. The author provides an exposition of the main results obtained in recent years by Soviet and other mathematicians in the theory of mappings with bounded distortion, an active direction in contemporary mathematics. The mathematical tools presented can be applied to a broad spectrum of problems that go beyond the context of the main topic of investigation. For a number of questions in the theory of partial differential equations and the theory of functions with generalized derivatives, this is the first time they have appeared in an internationally distributed monograph.
Book Synopsis Lectures on Mappings of Finite Distortion by : Stanislav Hencl
Download or read book Lectures on Mappings of Finite Distortion written by Stanislav Hencl and published by Springer. This book was released on 2014-01-24 with total page 182 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
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.
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.
Book Synopsis N-Dimensional Quasiconformal (QCf) Mappings by : Petru Caraman
Download or read book N-Dimensional Quasiconformal (QCf) Mappings written by Petru Caraman and published by CRC Press. This book was released on 1974 with total page 554 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Stability Theorems in Geometry and Analysis by : Yu.G. Reshetnyak
Download or read book Stability Theorems in Geometry and Analysis written by Yu.G. Reshetnyak and published by Springer Science & Business Media. This book was released on 2013-04-09 with total page 406 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is one of the first monographs to deal with the metric theory of spatial mappings and incorporates results in the theory of quasi-conformal, quasi-isometric and other mappings. The main subject is the study of the stability problem in Liouville's theorem on conformal mappings in space, which is representative of a number of problems on stability for transformation classes. To enable this investigation a wide range of mathematical tools has been developed which incorporate the calculus of variation, estimates for differential operators like Korn inequalities, properties of functions with bounded mean oscillation, etc. Results obtained by others researching similar topics are mentioned, and a survey is given of publications treating relevant questions or involving the technique proposed. This volume will be of great value to graduate students and researchers interested in geometric function theory.
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.
Book Synopsis The Interaction of Analysis and Geometry by : I͡Uriĭ Grigorʹevich Reshetni͡ak
Download or read book The Interaction of Analysis and Geometry written by I͡Uriĭ Grigorʹevich Reshetni͡ak and published by American Mathematical Soc.. This book was released on 2007 with total page 344 pages. Available in PDF, EPUB and Kindle. Book excerpt: The papers in this volume are based on talks given at the International Conference on Analysis and Geometry in honor of the 75th birthday of Yurii Reshetnyak (Novosibirsk, 2004). The topics include geometry of spaces with bounded curvature in the sense of Alexandrov, quasiconformal mappings and mappings with bounded distortion (quasiregular mappings), nonlinear potential theory, Sobolev spaces, spaces with fractional and generalized smoothness, variational problems, and other modern trends in these areas. Most articles are related to Reshetnyak's original works and demonstrate the vitality of his fundamental contribution in some important fields of mathematics such as the geometry in the ""large"", quasiconformal analysis, Sobolev spaces, potential theory and variational calculus.
Book Synopsis Nonlinear Potential Theory of Degenerate Elliptic Equations by : Juha Heinonen
Download or read book Nonlinear Potential Theory of Degenerate Elliptic Equations written by Juha Heinonen and published by Courier Dover Publications. This book was released on 2018-05-16 with total page 416 pages. Available in PDF, EPUB and Kindle. Book excerpt: A self-contained treatment appropriate for advanced undergraduates and graduate students, this text offers a detailed development of the necessary background for its survey of the nonlinear potential theory of superharmonic functions. 1993 edition.
Book Synopsis Value Distribution Theory by : I. Laine
Download or read book Value Distribution Theory written by I. Laine and published by Springer. This book was released on 2006-11-15 with total page 256 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis An Introduction to the Theory of Higher-Dimensional Quasiconformal Mappings by : Frederick W. Gehring
Download or read book An Introduction to the Theory of Higher-Dimensional Quasiconformal Mappings written by Frederick W. Gehring and published by American Mathematical Soc.. This book was released on 2017-05-03 with total page 116 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book offers a modern, up-to-date introduction to quasiconformal mappings from an explicitly geometric perspective, emphasizing both the extensive developments in mapping theory during the past few decades and the remarkable applications of geometric function theory to other fields, including dynamical systems, Kleinian groups, geometric topology, differential geometry, and geometric group theory. It is a careful and detailed introduction to the higher-dimensional theory of quasiconformal mappings from the geometric viewpoint, based primarily on the technique of the conformal modulus of a curve family. Notably, the final chapter describes the application of quasiconformal mapping theory to Mostow's celebrated rigidity theorem in its original context with all the necessary background. This book will be suitable as a textbook for graduate students and researchers interested in beginning to work on mapping theory problems or learning the basics of the geometric approach to quasiconformal mappings. Only a basic background in multidimensional real analysis is assumed.
Book Synopsis Sobolev Spaces on Metric Measure Spaces by : Juha Heinonen
Download or read book Sobolev Spaces on Metric Measure Spaces written by Juha Heinonen and published by Cambridge University Press. This book was released on 2015-02-05 with total page 447 pages. Available in PDF, EPUB and Kindle. Book excerpt: This coherent treatment from first principles is an ideal introduction for graduate students and a useful reference for experts.
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.
Book Synopsis Holomorphic Functions and Moduli I by : D. Drasin
Download or read book Holomorphic Functions and Moduli I written by D. Drasin and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 249 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Spring 1986 Program in Geometric Function Theory (GFT) at the Mathematical Sciences Research Institute (MSRI) brought together mathe maticians interested in Teichmiiller theory, quasiconformal mappings, Kleinian groups, univalent functions and value distribution. It included a large and stimulating Workshop, preceded by a mini-conference on String Theory attended by both mathematicians and physicists. These activities produced interesting results and fruitful interactions among the partici pants. These volumes represent only a portion of the papers that will even tually result from ideas developed in the offices and corridors of MSRI's elegant home. The Editors solicited contributions from all participants in the Program whether or not they gave a talk at the Workshop. Papers were also submit ted by mathematicians invited but unable to attend. All manuscripts were refereed. The articles included here cover a broad spectrum, representative of the activities during the semester. We have made an attempt to group them by subject, for the reader's convenience. The Editors take pleasure in thanking all participants, authors and ref erees for their work in producing these volumes. We are also grateful to the Scientific Advisory Council of MSRI for sup porting the Program in GFT. Finally thanks are due to the National Sci ence Foundation and those Universities (including Cornell, Michigan, Min nesota, Rutgers Newark, SUNY Stony Brook) who gave released time to faculty members to participate for extended periods in this program.
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.
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.
Book Synopsis Analysis and Topology by : Cabiria Andreian Cazacu
Download or read book Analysis and Topology written by Cabiria Andreian Cazacu and published by World Scientific. This book was released on 1998-11-06 with total page 736 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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
