Quasiconformal Mappings And Analysis
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| Author | : Peter Duren |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 379 |
| Release | : 2012-12-06 |
| Genre | : Mathematics |
| ISBN | : 1461206057 |
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 | : Jussi Väisälä |
| Publisher | : |
| Total Pages | : 158 |
| Release | : 1971 |
| Genre | : Conformal mapping |
| ISBN | : 9780387056487 |
| Author | : Lars Valerian Ahlfors |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 178 |
| Release | : 2006-07-14 |
| Genre | : Mathematics |
| ISBN | : 0821836447 |
Lars Ahlfors's Lectures on Quasiconformal Mappings, based on a course he gave at Harvard University in the spring term of 1964, was first published in 1966 and was soon recognized as the classic it was shortly destined to become. These lectures develop the theory of quasiconformal mappings from scratch, give a self-contained treatment of the Beltrami equation, and cover the basic properties of Teichmuller spaces, including the Bers embedding and the Teichmuller curve. It is remarkable how Ahlfors goes straight to the heart of the matter, presenting major results with a minimum set of prerequisites. Many graduate students and other mathematicians have learned the foundations of the theories of quasiconformal mappings and Teichmuller spaces from these lecture notes. This edition includes three new chapters. The first, written by Earle and Kra, describes further developments in the theory of Teichmuller spaces and provides many references to the vast literature on Teichmuller spaces and quasiconformal mappings. The second, by Shishikura, describes how quasiconformal mappings have revitalized the subject of complex dynamics. The third, by Hubbard, illustrates the role of these mappings in Thurston's theory of hyperbolic structures on 3-manifolds. Together, these three new chapters exhibit the continuing vitality and importance of the theory of quasiconformal mappings.
| Author | : Vesna Todorčević |
| Publisher | : Springer |
| Total Pages | : 163 |
| Release | : 2020-08-15 |
| Genre | : Mathematics |
| ISBN | : 9783030225933 |
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 | : Kari Astala |
| Publisher | : Princeton University Press |
| Total Pages | : 708 |
| Release | : 2009-01-18 |
| Genre | : Mathematics |
| ISBN | : 9780691137773 |
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 | : Alastair Fletcher |
| Publisher | : Oxford University Press, USA |
| Total Pages | : 208 |
| Release | : 2007 |
| Genre | : Mathematics |
| ISBN | : |
| Author | : Olli Lehto |
| Publisher | : Springer |
| Total Pages | : 0 |
| Release | : 2011-11-11 |
| Genre | : Mathematics |
| ISBN | : 9783642655159 |
The present text is a fairly direct translation of the German edition "Quasikonforme Abbildungen" published in 1965. During the past decade the theory of quasi conformal mappings in the plane has remained relatively stable. We felt, therefore, that major changes were not necessarily required in the text. In view of the recent progress in the higher-dimensional theory we found it preferable to indicate the two-dimensional case in the title. Our sincere thanks are due to K. W. Lucas, who did the major part of the translation work. In shaping the final form of the text with him we received many valuable suggestions from A. J. Lohwater. We are indebted to Anja Aaltonen and Pentti Dyyster for the prepara tion of the manuscript, and to Timo Erkama and Tuomas Sorvali for the careful reading and correction of the proofs. Finally, we should like to express our thanks to Springer-Verlag for their friendly coopera tion in the production of this volume.
| Author | : Seppo Rickman |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 221 |
| Release | : 2012-12-06 |
| Genre | : Mathematics |
| ISBN | : 3642782019 |
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 | : Bodil Branner |
| Publisher | : Cambridge University Press |
| Total Pages | : 433 |
| Release | : 2014-01-23 |
| Genre | : Mathematics |
| ISBN | : 1107042917 |
A comprehensive introduction to quasiconformal surgery in holomorphic dynamics. Contains a wide variety of applications and illustrations.
| Author | : Reiner Kuhnau |
| Publisher | : Elsevier |
| Total Pages | : 549 |
| Release | : 2002-12-05 |
| Genre | : Mathematics |
| ISBN | : 0080532810 |
Geometric Function Theory is a central part of Complex Analysis (one complex variable). The Handbook of Complex Analysis - Geometric Function Theory deals with this field and its many ramifications and relations to other areas of mathematics and physics. The theory of conformal and quasiconformal mappings plays a central role in this Handbook, for example a priori-estimates for these mappings which arise from solving extremal problems, and constructive methods are considered. As a new field the theory of circle packings which goes back to P. Koebe is included. The Handbook should be useful for experts as well as for mathematicians working in other areas, as well as for physicists and engineers.· 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)
