Conformal Geometry and Quasiregular Mappings
Title | Conformal Geometry and Quasiregular Mappings PDF eBook |
Author | Matti Vuorinen |
Publisher | Springer |
Pages | 228 |
Release | 2006-11-15 |
Genre | Mathematics |
ISBN | 3540392076 |
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.
Conformal Geometry
Title | Conformal Geometry PDF eBook |
Author | Ravi S. Kulkarni |
Publisher | Springer-Verlag |
Pages | 245 |
Release | 2013-03-09 |
Genre | Mathematics |
ISBN | 3322906167 |
Quasiconformal Space Mappings
Title | Quasiconformal Space Mappings PDF eBook |
Author | Matti Vuorinen |
Publisher | Springer |
Pages | 156 |
Release | 2006-11-14 |
Genre | Mathematics |
ISBN | 3540470611 |
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.
The Theory and Practice of Conformal Geometry
Title | The Theory and Practice of Conformal Geometry PDF eBook |
Author | Steven G. Krantz |
Publisher | Courier Dover Publications |
Pages | 308 |
Release | 2016-02-17 |
Genre | Mathematics |
ISBN | 0486793443 |
An expert on conformal geometry introduces some of the subject's modern developments. Topics include the Riemann mapping theorem, invariant metrics, automorphism groups, harmonic measure, extremal length, analytic capacity, invariant geometry, and more. 2016 edition.
Computational Conformal Geometry
Title | Computational Conformal Geometry PDF eBook |
Author | Xianfeng David Gu |
Publisher | |
Pages | 324 |
Release | 2008 |
Genre | CD-ROMs |
ISBN |
Conformal Maps And Geometry
Title | Conformal Maps And Geometry PDF eBook |
Author | Dmitry Beliaev |
Publisher | World Scientific |
Pages | 240 |
Release | 2019-11-19 |
Genre | Mathematics |
ISBN | 178634615X |
'I very much enjoyed reading this book … Each chapter comes with well thought-out exercises, solutions to which are given at the end of the chapter. Conformal Maps and Geometry presents key topics in geometric function theory and the theory of univalent functions, and also prepares the reader to progress to study the SLE. It succeeds admirably on both counts.'MathSciNetGeometric function theory is one of the most interesting parts of complex analysis, an area that has become increasingly relevant as a key feature in the theory of Schramm-Loewner evolution.Though Riemann mapping theorem is frequently explored, there are few texts that discuss general theory of univalent maps, conformal invariants, and Loewner evolution. This textbook provides an accessible foundation of the theory of conformal maps and their connections with geometry.It offers a unique view of the field, as it is one of the first to discuss general theory of univalent maps at a graduate level, while introducing more complex theories of conformal invariants and extremal lengths. Conformal Maps and Geometry is an ideal resource for graduate courses in Complex Analysis or as an analytic prerequisite to study the theory of Schramm-Loewner evolution.
Conformally Invariant Metrics and Quasiconformal Mappings
Title | Conformally Invariant Metrics and Quasiconformal Mappings PDF eBook |
Author | Parisa Hariri |
Publisher | Springer Nature |
Pages | 504 |
Release | 2020-04-11 |
Genre | Mathematics |
ISBN | 3030320685 |
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.