Conformal Geometry
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Topological Differential And Conformal Geometry Of Surfaces
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Author : Norbert A'Campo
language : en
Publisher: Springer
Release Date : 2021-10-28
Topological Differential And Conformal Geometry Of Surfaces written by Norbert A'Campo and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-10-28 with Mathematics categories.
This book provides an introduction to the main geometric structures that are carried by compact surfaces, with an emphasis on the classical theory of Riemann surfaces. It first covers the prerequisites, including the basics of differential forms, the Poincaré Lemma, the Morse Lemma, the classification of compact connected oriented surfaces, Stokes’ Theorem, fixed point theorems and rigidity theorems. There is also a novel presentation of planar hyperbolic geometry. Moving on to more advanced concepts, it covers topics such as Riemannian metrics, the isometric torsion-free connection on vector fields, the Ansatz of Koszul, the Gauss–Bonnet Theorem, and integrability. These concepts are then used for the study of Riemann surfaces. One of the focal points is the Uniformization Theorem for compact surfaces, an elementary proof of which is given via a property of the energy functional. Among numerous other results, there is also a proof of Chow’s Theorem on compact holomorphic submanifolds in complex projective spaces. Based on lecture courses given by the author, the book will be accessible to undergraduates and graduates interested in the analytic theory of Riemann surfaces.
Computational Conformal Geometry
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Author : Xianfeng David Gu
language : en
Publisher:
Release Date : 2008
Computational Conformal Geometry written by Xianfeng David Gu and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008 with CD-ROMs categories.
"Computational conformal geometry is an emerging inter-disciplinary field, which applies algebraic topology, differential geometry and Riemann surface theories in geometric modelling, computer graphics, computer vision, medical imaging, visualization, scientifice computations and many other engineering fields."--Back cover.
Conformal Geometry Of Discrete Groups And Manifolds
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Author : Boris N. Apanasov
language : en
Publisher: Walter de Gruyter
Release Date : 2011-06-24
Conformal Geometry Of Discrete Groups And Manifolds written by Boris N. Apanasov and has been published by Walter de Gruyter this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-06-24 with Mathematics categories.
The aim of the Expositions is to present new and important developments in pure and applied mathematics. Well established in the community over more than two decades, the series offers a large library of mathematical works, including several important classics. The volumes supply thorough and detailed expositions of the methods and ideas essential to the topics in question. In addition, they convey their relationships to other parts of mathematics. The series is addressed to advanced readers interested in a thorough study of the subject. Editorial Board Lev Birbrair, Universidade Federal do Ceará, Fortaleza, Brasil Walter D. Neumann, Columbia University, New York, USA Markus J. Pflaum, University of Colorado, Boulder, USA Dierk Schleicher, Jacobs University, Bremen, Germany Katrin Wendland, University of Freiburg, Germany Honorary Editor Victor P. Maslov, Russian Academy of Sciences, Moscow, Russia Titles in planning include Yuri A. Bahturin, Identical Relations in Lie Algebras (2019) Yakov G. Berkovich, Lev G. Kazarin, and Emmanuel M. Zhmud', Characters of Finite Groups, Volume 2 (2019) Jorge Herbert Soares de Lira, Variational Problems for Hypersurfaces in Riemannian Manifolds (2019) Volker Mayer, Mariusz Urbański, and Anna Zdunik, Random and Conformal Dynamical Systems (2021) Ioannis Diamantis, Boštjan Gabrovšek, Sofia Lambropoulou, and Maciej Mroczkowski, Knot Theory of Lens Spaces (2021)
The Theory And Practice Of Conformal Geometry
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Author : Steven G. Krantz
language : en
Publisher: Courier Dover Publications
Release Date : 2016-02-17
The Theory And Practice Of Conformal Geometry written by Steven G. Krantz and has been published by Courier Dover Publications this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-02-17 with Mathematics categories.
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.
Conformal Geometry
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Author : Miao Jin
language : en
Publisher: Springer
Release Date : 2018-04-10
Conformal Geometry written by Miao Jin and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-04-10 with Computers categories.
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.
The Theory And Practice Of Conformal Geometry
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Author : Steven G. Krantz
language : en
Publisher: Courier Dover Publications
Release Date : 2016-03-17
The Theory And Practice Of Conformal Geometry written by Steven G. Krantz and has been published by Courier Dover Publications this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-03-17 with Mathematics categories.
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.
Energy Of Knots And Conformal Geometry
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Author : Jun O'Hara
language : en
Publisher: World Scientific
Release Date : 2003
Energy Of Knots And Conformal Geometry written by Jun O'Hara and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003 with Mathematics categories.
Energy of knots is a theory that was introduced to create a OC canonical configurationOCO of a knot OCo a beautiful knot which represents its knot type. This book introduces several kinds of energies, and studies the problem of whether or not there is a OC canonical configurationOCO of a knot in each knot type. It also considers this problems in the context of conformal geometry. The energies presented in the book are defined geometrically. They measure the complexity of embeddings and have applications to physical knotting and unknotting through numerical experiments. Contents: In Search of the OC Optimal EmbeddingOCO of a Knot: -Energy Functional E (); On E (2); L p Norm Energy with Higher Index; Numerical Experiments; Stereo Pictures of E (2) Minimizers; Energy of Knots in a Riemannian Manifold; Physical Knot Energies; Energy of Knots from a Conformal Geometric Viewpoint: Preparation from Conformal Geometry; The Space of Non-Trivial Spheres of a Knot; The Infinitesimal Cross Ratio; The Conformal Sin Energy E sin (c) Measure of Non-Trivial Spheres; Appendices: Generalization of the Gauss Formula for the Linking Number; The 3-Tuple Map to the Set of Circles in S 3; Conformal Moduli of a Solid Torus; Kirchhoff Elastica; Open Problems and Dreams. Readership: Graduate students and researchers in geometry & topology and numerical & computational mathematics."
Conformal Differential Geometry
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Author : Helga Baum
language : en
Publisher: Springer Science & Business Media
Release Date : 2011-01-28
Conformal Differential Geometry written by Helga Baum 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 2011-01-28 with Mathematics categories.
Conformal invariants (conformally invariant tensors, conformally covariant differential operators, conformal holonomy groups etc.) are of central significance in differential geometry and physics. Well-known examples of such operators are the Yamabe-, the Paneitz-, the Dirac- and the twistor operator. The aim of the seminar was to present the basic ideas and some of the recent developments around Q-curvature and conformal holonomy. The part on Q-curvature discusses its origin, its relevance in geometry, spectral theory and physics. Here the influence of ideas which have their origin in the AdS/CFT-correspondence becomes visible. The part on conformal holonomy describes recent classification results, its relation to Einstein metrics and to conformal Killing spinors, and related special geometries.
Conformal Geometry And Quasiregular Mappings
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Author : Matti Vuorinen
language : en
Publisher: Springer
Release Date : 2006-11-15
Conformal Geometry And Quasiregular Mappings written by Matti Vuorinen and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-11-15 with Mathematics categories.
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 Representation
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Author : Constantin Caratheodory
language : en
Publisher: Courier Corporation
Release Date : 1998-01-01
Conformal Representation written by Constantin Caratheodory and has been published by Courier Corporation this book supported file pdf, txt, epub, kindle and other format this book has been release on 1998-01-01 with Mathematics categories.
Comprehensive introduction discusses the Möbius transformation, non-Euclidean geometry, elementary transformations, Schwarz's Lemma, transformation of the frontier and closed surfaces, and the general theorem of uniformization. Detailed proofs.