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Author: Steven G. Krantz Publisher: Courier Dover Publications ISBN: 0486810321 Category : Mathematics Languages : en Pages : 308
Book Description
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: Steven G. Krantz Publisher: Courier Dover Publications ISBN: 0486810321 Category : Mathematics Languages : en Pages : 308
Book Description
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: 3540392076 Category : Mathematics Languages : en Pages : 228
Book Description
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: Miao Jin Publisher: Springer ISBN: 3319753320 Category : Computers Languages : en Pages : 318
Book Description
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: Francis E. Burstall Publisher: Springer ISBN: 3540453016 Category : Mathematics Languages : en Pages : 98
Book Description
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: Dmitry Beliaev Publisher: World Scientific ISBN: 178634615X Category : Mathematics Languages : en Pages : 240
Book Description
'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: Abbas Bahri Publisher: Imperial College Press ISBN: 186094860X Category : Mathematics Languages : en Pages : 522
Book Description
This book presents a new front of research in conformal geometry, on sign-changing Yamabe-type problems and contact form geometry in particular. New ground is broken with the establishment of a Morse lemma at infinity for sign-changing Yamabe-type problems. This family of problems, thought to be out of reach a few years ago, becomes a family of problems which can be studied: the book lays the foundation for a program of research in this direction. In contact form geometry, a cousin of symplectic geometry, the authors prove a fundamental result of compactness in a variational problem on Legrendrian curves, which allows one to define a homology associated to a contact structure and a vector field of its kernel on a three-dimensional manifold. The homology is invariant under deformation of the contact form, and can be read on a sub-Morse complex of the Morse complex of the variational problem built with the periodic orbits of the Reeb vector-field. This book introduces, therefore, a practical tool in the field, and this homology becomes computable.
Author: Steven G. Krantz
Author: Steven G. Krantz
Author: Matti Vuorinen
Author: Miao Jin
Author: Francis E. Burstall
Author: Ravi S. Kulkarni
Author: Dmitry Beliaev
Author: Boris Nikolaevich Apanasov
Author: Xianfeng David Gu
Author: Tammo Diemer
Author: Abbas Bahri