Conformal Maps And Geometry
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| Author | : Dmitry Beliaev |
| Publisher | : World Scientific |
| Total 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.
| Author | : Prem K. Kythe |
| Publisher | : CRC Press |
| Total Pages | : 943 |
| Release | : 2019-03-04 |
| Genre | : Mathematics |
| ISBN | : 1351718738 |
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 | : Xianfeng David Gu |
| Publisher | : |
| Total Pages | : 324 |
| Release | : 2008 |
| Genre | : CD-ROMs |
| ISBN | : |
| Author | : David E. Blair |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 130 |
| Release | : 2000-08-17 |
| Genre | : Mathematics |
| ISBN | : 0821826360 |
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 | : Maks A. Akivis |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 272 |
| Release | : 2004 |
| Genre | : Mathematics |
| ISBN | : 0387404635 |
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 | : Miao Jin |
| Publisher | : Springer |
| Total Pages | : 318 |
| Release | : 2018-04-10 |
| Genre | : Computers |
| ISBN | : 3319753320 |
This book offers an essential overview of computational conformal geometry applied to fundamental problems in specific engineering fields. It introduces readers to conformal geometry theory and discusses implementation issues from an engineering perspective. The respective chapters explore fundamental problems in specific fields of application, and detail how computational conformal geometric methods can be used to solve them in a theoretically elegant and computationally efficient way. The fields covered include computer graphics, computer vision, geometric modeling, medical imaging, and wireless sensor networks. Each chapter concludes with a summary of the material covered and suggestions for further reading, and numerous illustrations and computational algorithms complement the text. The book draws on courses given by the authors at the University of Louisiana at Lafayette, the State University of New York at Stony Brook, and Tsinghua University, and will be of interest to senior undergraduates, graduates and researchers in computer science, applied mathematics, and engineering.
| Author | : Sorin Dragomir |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 332 |
| Release | : 2012-12-06 |
| Genre | : Mathematics |
| ISBN | : 1461220262 |
. E C, 0 1'1 1, and n E Z, n ~ 2. Let~.. be the O-dimensional Lie n group generated by the transformation z ~ >.z, z E C - {a}. Then (cf.
| Author | : Erwin Kreyszig |
| Publisher | : Courier Corporation |
| Total Pages | : 384 |
| Release | : 2013-04-26 |
| Genre | : Mathematics |
| ISBN | : 0486318621 |
An introductory textbook on the differential geometry of curves and surfaces in 3-dimensional Euclidean space, presented in its simplest, most essential form. With problems and solutions. Includes 99 illustrations.
| Author | : Tadeusz Iwaniec |
| Publisher | : Clarendon Press |
| Total Pages | : 576 |
| Release | : 2001 |
| Genre | : Language Arts & Disciplines |
| ISBN | : 9780198509295 |
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.
| Author | : John M. Mackay |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 162 |
| Release | : 2010 |
| Genre | : Mathematics |
| ISBN | : 0821852299 |
Conformal dimension measures the extent to which the Hausdorff dimension of a metric space can be lowered by quasisymmetric deformations. Introduced by Pansu in 1989, this concept has proved extremely fruitful in a diverse range of areas, including geometric function theory, conformal dynamics, and geometric group theory. This survey leads the reader from the definitions and basic theory through to active research applications in geometric function theory, Gromov hyperbolic geometry, and the dynamics of rational maps, amongst other areas. It reviews the theory of dimension in metric spaces and of deformations of metric spaces. It summarizes the basic tools for estimating conformal dimension and illustrates their application to concrete problems of independent interest. Numerous examples and proofs are provided. Working from basic definitions through to current research areas, this book can be used as a guide for graduate students interested in this field, or as a helpful survey for experts. Background needed for a potential reader of the book consists of a working knowledge of real and complex analysis on the level of first- and second-year graduate courses.
