Moduli Of Families Of Curves For Conformal And Quasiconformal Mappings
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| Author | : Alexander Vasil'ev |
| Publisher | : Springer |
| Total Pages | : 222 |
| Release | : 2004-10-19 |
| Genre | : Mathematics |
| ISBN | : 3540454373 |
Download Moduli of Families of Curves for Conformal and Quasiconformal Mappings Book in PDF, Epub and Kindle
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.
| Author | : Alexander Vasil'ev |
| Publisher | : |
| Total Pages | : 46 |
| Release | : 1998 |
| Genre | : |
| ISBN | : |
Download Moduli of Families of Curves and Quasiconformal Mappings Book in PDF, Epub and Kindle
| Author | : Parisa Hariri |
| Publisher | : Springer Nature |
| Total Pages | : 504 |
| Release | : 2020-04-11 |
| Genre | : Mathematics |
| ISBN | : 3030320685 |
Download Conformally Invariant Metrics and Quasiconformal Mappings Book in PDF, Epub and Kindle
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 | : Vesna Todorčević |
| Publisher | : Springer |
| Total Pages | : 163 |
| Release | : 2019-07-24 |
| Genre | : Mathematics |
| ISBN | : 3030225917 |
Download Harmonic Quasiconformal Mappings and Hyperbolic Type Metrics Book in PDF, Epub and Kindle
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 | : M. Hazewinkel |
| Publisher | : Springer |
| Total Pages | : 967 |
| Release | : 2013-12-01 |
| Genre | : Mathematics |
| ISBN | : 1489937951 |
Download Encyclopaedia of Mathematics Book in PDF, Epub and Kindle
| Author | : Frederick W. Gehring |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 442 |
| Release | : 2017-05-03 |
| Genre | : Mathematics |
| ISBN | : 0821843605 |
Download An Introduction to the Theory of Higher-Dimensional Quasiconformal Mappings Book in PDF, Epub and Kindle
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.
| Author | : Michiel Hazewinkel |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 499 |
| Release | : 2013-12-01 |
| Genre | : Mathematics |
| ISBN | : 940095994X |
Download Encyclopaedia of Mathematics Book in PDF, Epub and Kindle
| Author | : Reiner Kuhnau |
| Publisher | : Elsevier |
| Total Pages | : 876 |
| Release | : 2004-12-09 |
| Genre | : Mathematics |
| ISBN | : 0080495176 |
Download Handbook of Complex Analysis Book in PDF, Epub and Kindle
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).
| Author | : Matti Vuorinen |
| Publisher | : Springer |
| Total Pages | : 156 |
| Release | : 2006-11-14 |
| Genre | : Mathematics |
| ISBN | : 3540470611 |
Download Quasiconformal Space Mappings Book in PDF, Epub and Kindle
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 | : Tadeusz Iwaniec |
| Publisher | : Clarendon Press |
| Total Pages | : 576 |
| Release | : 2001 |
| Genre | : Language Arts & Disciplines |
| ISBN | : 9780198509295 |
Download Geometric Function Theory and Non-linear Analysis Book in PDF, Epub and Kindle
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.
