Boundary Behaviour Of Conformal Maps
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Boundary Behaviour Of Conformal Maps
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Author : Christian Pommerenke
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-04-09
Boundary Behaviour Of Conformal Maps written by Christian Pommerenke 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 2013-04-09 with Mathematics categories.
We study the boundary behaviour of a conformal map of the unit disk onto an arbitrary simply connected plane domain. A principal aim of the theory is to obtain a one-to-one correspondence between analytic properties of the function and geometrie properties of the domain. In the classical applications of conformal mapping, the domain is bounded by a piecewise smooth curve. In many recent applications however, the domain has a very bad boundary. It may have nowhere a tangent as is the case for Julia sets. Then the conformal map has many unexpected properties, for instance almost all the boundary is mapped onto almost nothing and vice versa. The book is meant for two groups of users. (1) Graduate students and others who, at various levels, want to learn about conformal mapping. Most sections contain exercises to test the understand ing. They tend to be fairly simple and only a few contain new material. Pre requisites are general real and complex analyis including the basic facts about conformal mapping (e.g. AhI66a). (2) Non-experts who want to get an idea of a particular aspect of confor mal mapping in order to find something useful for their work. Most chapters therefore begin with an overview that states some key results avoiding tech nicalities. The book is not meant as an exhaustive survey of conformal mapping. Several important aspects had to be omitted, e.g. numerical methods (see e.g.
Boundary Behaviour Of Conformal Maps
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Author : C. Pommerenke
language : en
Publisher:
Release Date : 1992
Boundary Behaviour Of Conformal Maps written by C. Pommerenke and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1992 with categories.
Studies Of The Behavior Of The Mapping Function On The Boundary In Conformal Mapping
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Author : James Edgar Thompson
language : en
Publisher:
Release Date : 1951
Studies Of The Behavior Of The Mapping Function On The Boundary In Conformal Mapping written by James Edgar Thompson and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1951 with Conformal mapping categories.
A Conformal Mapping Technique For Infinitely Connected Regions
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Author : Maynard G. Arsove
language : en
Publisher: American Mathematical Soc.
Release Date : 1970
A Conformal Mapping Technique For Infinitely Connected Regions written by Maynard G. Arsove and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 1970 with Boundary value problems categories.
Methods of classical analysis devised originally for the disc are here extended to more general plane regions by the use of Green's lines, the Green's mapping, and an ideal boundary structure generalizing the prime-end structure of Carathéodory. The regions admitted include all bounded finitely connected regions, as well as a broad class of infinitely connected regions. Since certain modifications in the Brelot-Choquet theory are needed to allow for singular Green's lines, an independent development of the theory of Green's lines is given, based on properties of the Green's mapping. These techniques make possible the introduction of a generalized Poisson kernel and integral defined in terms of Green's lines.
Conformal Mappings And Boundary Value Problems
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Author : Guo-Chun Wen
language : en
Publisher: American Mathematical Soc.
Release Date :
Conformal Mappings And Boundary Value Problems written by Guo-Chun Wen and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on with Mathematics categories.
Translated from the Chinese. Conformal mapping and boundary value problems are two major branches of complex function theory. The former is the geometric theory of analytic functions, and the latter is the analysis theory governing the close relationship between abstract theory and many concrete problems. Topics include applications of Cauchy type integrals, the Hilbert boundary value problem, quasiconformal mappings, and basic boundary value problems for harmonic functions. Annotation copyright by Book News, Inc., Portland, OR
Foundations Of Analysis In The Complex Domain
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Author : Ilja Černý
language : en
Publisher: Prentice Hall
Release Date : 1992
Foundations Of Analysis In The Complex Domain written by Ilja Černý and has been published by Prentice Hall this book supported file pdf, txt, epub, kindle and other format this book has been release on 1992 with Mathematics categories.
This book looks at the boundary behaviour of conformal mappings, including an introduction to the topic of prime-ends theory. It includes an exposition of the theory of analytical functions, incorporating operations and reviewing the applications of both theories to vector fields.
Handbook Of Conformal Mappings And Applications
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Author : Prem K. Kythe
language : en
Publisher: CRC Press
Release Date : 2019-03-04
Handbook Of Conformal Mappings And Applications written by Prem K. Kythe and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-03-04 with Mathematics categories.
The subject of conformal mappings is a major part of geometric function theory that gained prominence after the publication of the Riemann mapping theorem — for every simply connected domain of the extended complex plane there is a univalent and meromorphic function that maps such a domain conformally onto the unit disk. The Handbook of Conformal Mappings and Applications is a compendium of at least all known conformal maps to date, with diagrams and description, and all possible applications in different scientific disciplines, such as: fluid flows, heat transfer, acoustics, electromagnetic fields as static fields in electricity and magnetism, various mathematical models and methods, including solutions of certain integral equations.
Conformal Mapping
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Author : Ludwig Bieberbach
language : en
Publisher: American Mathematical Soc.
Release Date : 2000
Conformal Mapping written by Ludwig Bieberbach and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2000 with Mathematics categories.
Translated from the fourth German edition by F. Steinhardt, with an expanded Bibliography.
Conformal Maps And Geometry
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Author : Dmitry Beliaev
language : en
Publisher: World Scientific
Release Date : 2019-11-19
Conformal Maps And Geometry written by Dmitry Beliaev and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-11-19 with Mathematics categories.
'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.
Moduli Of Families Of Curves For Conformal And Quasiconformal Mappings
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Author : Alexander Vasil'ev
language : en
Publisher: Springer
Release Date : 2004-10-20
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 2004-10-20 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.