Conformal Invariants Inequalities And Quasiconformal Maps
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Conformal Invariants Inequalities And Quasiconformal Maps
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Author : Glen D. Anderson
language : en
Publisher: Wiley-Interscience
Release Date : 1997
Conformal Invariants Inequalities And Quasiconformal Maps written by Glen D. Anderson and has been published by Wiley-Interscience this book supported file pdf, txt, epub, kindle and other format this book has been release on 1997 with Mathematics categories.
Disk contains: information on Conformal Invariants Software which accompanies the text.
Conformally Invariant Metrics And Quasiconformal Mappings
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Author : Parisa Hariri
language : en
Publisher: Springer Nature
Release Date : 2020-04-11
Conformally Invariant Metrics And Quasiconformal Mappings written by Parisa Hariri and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-04-11 with Mathematics categories.
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.
Harmonic Quasiconformal Mappings And Hyperbolic Type Metrics
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Author : Vesna Todorčević
language : en
Publisher: Springer
Release Date : 2019-07-24
Harmonic Quasiconformal Mappings And Hyperbolic Type Metrics written by Vesna Todorčević and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-07-24 with Mathematics categories.
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.
Moduli Of Families Of Curves For Conformal And Quasiconformal Mappings
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Author : Alexander Vasil'ev
language : en
Publisher: Springer
Release Date : 2004-10-19
Moduli Of Families Of Curves For Conformal And Quasiconformal Mappings written by Alexander Vasil'ev and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004-10-19 with Mathematics categories.
The monograph is concerned with the modulus of families of curves on Riemann surfaces and its applications to extremal problems for conformal, quasiconformal mappings, and the extension of the modulus onto Teichmüller spaces. The main part of the monograph deals with extremal problems for compact classes of univalent conformal and quasiconformal mappings. Many of them are grouped around two-point distortion theorems. Montel's functions and functions with fixed angular derivatives are also considered. The last portion of problems is directed to the extension of the modulus varying the complex structure of the underlying Riemann surface that sheds some new light on the metric problems of Teichmüller spaces.
Quasiconformal Space Mappings
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Author : Matti Vuorinen
language : en
Publisher: Springer
Release Date : 2006-11-14
Quasiconformal Space Mappings written by Matti Vuorinen and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-11-14 with Mathematics categories.
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.
Handbook Of Complex Analysis
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Author : Reiner Kuhnau
language : en
Publisher: Elsevier
Release Date : 2004-12-09
Handbook Of Complex Analysis written by Reiner Kuhnau and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004-12-09 with Mathematics categories.
Geometric Function Theory is that part of Complex Analysis which covers the theory of conformal and quasiconformal mappings. Beginning with the classical Riemann mapping theorem, there is a lot of existence theorems for canonical conformal mappings. On the other side there is an extensive theory of qualitative properties of conformal and quasiconformal mappings, concerning mainly a prior estimates, so called distortion theorems (including the Bieberbach conjecture with the proof of the Branges). Here a starting point was the classical Scharz lemma, and then Koebe's distortion theorem. There are several connections to mathematical physics, because of the relations to potential theory (in the plane). The Handbook of Geometric Function Theory contains also an article about constructive methods and further a Bibliography including applications eg: to electroxtatic problems, heat conduction, potential flows (in the plane). · A collection of independent survey articles in the field of GeometricFunction Theory · Existence theorems and qualitative properties of conformal and quasiconformal mappings · A bibliography, including many hints to applications in electrostatics, heat conduction, potential flows (in the plane).
Conformal Geometry Of Discrete Groups And Manifolds
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Author : Boris N. Apanasov
language : en
Publisher: Walter de Gruyter
Release Date : 2011-06-24
Conformal Geometry Of Discrete Groups And Manifolds written by Boris N. Apanasov and has been published by Walter de Gruyter this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-06-24 with Mathematics categories.
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
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Author : Peter Duren
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Quasiconformal Mappings And Analysis written by Peter Duren and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
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.
Conformal Geometry And Quasiregular Mappings
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Author : Matti Vuorinen
language : en
Publisher: Springer
Release Date : 2006-11-15
Conformal Geometry And Quasiregular Mappings written by Matti Vuorinen and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-11-15 with Mathematics categories.
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.
Encyclopaedia Of Mathematics Supplement Iii
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Author : Michiel Hazewinkel
language : en
Publisher: Springer Science & Business Media
Release Date : 2007-11-23
Encyclopaedia Of Mathematics Supplement Iii written by Michiel Hazewinkel and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007-11-23 with Mathematics categories.
This is the third supplementary volume to Kluwer's highly acclaimed twelve-volume Encyclopaedia of Mathematics. This additional volume contains nearly 500 new entries written by experts and covers developments and topics not included in the previous volumes. These entries are arranged alphabetically throughout and a detailed index is included. This supplementary volume enhances the existing twelve volumes, and together, these thirteen volumes represent the most authoritative, comprehensive and up-to-date Encyclopaedia of Mathematics available.