Conformal Maps And Geometry

Author : Dmitry Beliaev
Publisher : World Scientific
ISBN 13 : 178634615X
Total Pages : 240 pages
Book Rating : 4.55/5 ( download)

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Download or read book Conformal Maps And Geometry written by Dmitry Beliaev and published by World Scientific. This book was released on 2019-11-19 with total page 240 pages. Available in PDF, EPUB and Kindle. Book excerpt: '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.

Author : Prem K. Kythe
Publisher : CRC Press
ISBN 13 : 1351718738
Total Pages : 943 pages
Book Rating : 4.38/5 ( download)

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Download or read book Handbook of Conformal Mappings and Applications written by Prem K. Kythe and published by CRC Press. This book was released on 2019-03-04 with total page 943 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Author : David E. Blair
Publisher : American Mathematical Soc.
ISBN 13 : 0821826360
Total Pages : 130 pages
Book Rating : 4.62/5 ( download)

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Download or read book Inversion Theory and Conformal Mapping written by David E. Blair and published by American Mathematical Soc.. This book was released on 2000-08-17 with total page 130 pages. Available in PDF, EPUB and Kindle. Book excerpt: It is rarely taught in an undergraduate or even graduate curriculum that the only conformal maps in Euclidean space of dimension greater than two are those generated by similarities and inversions in spheres. This is in stark contrast to the wealth of conformal maps in the plane. The principal aim of this text is to give a treatment of this paucity of conformal maps in higher dimensions. The exposition includes both an analytic proof in general dimension and a differential-geometric proof in dimension three. For completeness, enough complex analysis is developed to prove the abundance of conformal maps in the plane. In addition, the book develops inversion theory as a subject, along with the auxiliary theme of circle-preserving maps. A particular feature is the inclusion of a paper by Caratheodory with the remarkable result that any circle-preserving transformation is necessarily a Mobius transformation, not even the continuity of the transformation is assumed. The text is at the level of advanced undergraduates and is suitable for a capstone course, topics course, senior seminar or independent study. Students and readers with university courses in differential geometry or complex analysis bring with them background to build on, but such courses are not essential prerequisites.

Author : Steven G. Krantz
Publisher : Courier Dover Publications
ISBN 13 : 0486810321
Total Pages : 304 pages
Book Rating : 4.24/5 ( download)

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Download or read book The Theory and Practice of Conformal Geometry written by Steven G. Krantz and published by Courier Dover Publications. This book was released on 2016-03-17 with total page 304 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this original text, prolific mathematics author Steven G. Krantz addresses conformal geometry, a subject that has occupied him for four decades and for which he helped to develop some of the modern theory. This book takes readers with a basic grounding in complex variable theory to the forefront of some of the current approaches to the topic. "Along the way," the author notes in his Preface, "the reader will be exposed to some beautiful function theory and also some of the rudiments of geometry and analysis that make this subject so vibrant and lively." More up-to-date and accessible to advanced undergraduates than most of the other books available in this specific field, the treatment discusses the history of this active and popular branch of mathematics as well as recent developments. Topics include the Riemann mapping theorem, invariant metrics, normal families, automorphism groups, the Schwarz lemma, harmonic measure, extremal length, analytic capacity, and invariant geometry. A helpful Bibliography and Index complete the text.

Author : Matti Vuorinen
Publisher : Springer
ISBN 13 : 3540392076
Total Pages : 228 pages
Book Rating : 4.71/5 ( download)

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Download or read book Conformal Geometry and Quasiregular Mappings written by Matti Vuorinen and published by Springer. This book was released on 2006-11-15 with total page 228 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Author : Francis E. Burstall
Publisher : Springer
ISBN 13 : 3540453016
Total Pages : 96 pages
Book Rating : 4.17/5 ( download)

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Download or read book Conformal Geometry of Surfaces in S4 and Quaternions written by Francis E. Burstall and published by Springer. This book was released on 2004-10-20 with total page 96 pages. Available in PDF, EPUB and Kindle. Book excerpt: The conformal geometry of surfaces recently developed by the authors leads to a unified understanding of algebraic curve theory and the geometry of surfaces on the basis of a quaternionic-valued function theory. The book offers an elementary introduction to the subject but takes the reader to rather advanced topics. Willmore surfaces in the foursphere, their Bäcklund and Darboux transforms are covered, and a new proof of the classification of Willmore spheres is given.

Author : Maks A. Akivis
Publisher : Springer Science & Business Media
ISBN 13 : 0387215115
Total Pages : 272 pages
Book Rating : 4.12/5 ( download)

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Download or read book Differential Geometry of Varieties with Degenerate Gauss Maps written by Maks A. Akivis and published by Springer Science & Business Media. This book was released on 2006-04-18 with total page 272 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book surveys the differential geometry of varieties with degenerate Gauss maps, using moving frames and exterior differential forms as well as tensor methods. The authors illustrate the structure of varieties with degenerate Gauss maps, determine the singular points and singular varieties, find focal images and construct a classification of the varieties with degenerate Gauss maps.

Author : Xianfeng David Gu
Publisher :
ISBN 13 :
Total Pages : 324 pages
Book Rating : 4.97/5 ( download)

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Download or read book Computational Conformal Geometry written by Xianfeng David Gu and published by . This book was released on 2008 with total page 324 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Author : Christian Pommerenke
Publisher : Springer Science & Business Media
ISBN 13 : 3662027704
Total Pages : 307 pages
Book Rating : 4.07/5 ( download)

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Download or read book Boundary Behaviour of Conformal Maps written by Christian Pommerenke and published by Springer Science & Business Media. This book was released on 2013-04-09 with total page 307 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Author : Ravi S. Kulkarni
Publisher : Springer-Verlag
ISBN 13 : 3322906167
Total Pages : 245 pages
Book Rating : 4.68/5 ( download)

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Download or read book Conformal Geometry written by Ravi S. Kulkarni and published by Springer-Verlag. This book was released on 2013-03-09 with total page 245 pages. Available in PDF, EPUB and Kindle. Book excerpt: