Conformal Geometry

Author : Matti Vuorinen
Publisher : Springer
Page : 228 pages
File Size : 41,9 Mb
Release : 2006-11-15
Category : Mathematics
ISBN : 9783540392071

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Conformal Geometry and Quasiregular Mappings by Matti Vuorinen Pdf

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 : Norbert A'Campo
Publisher : Springer Nature
Page : 282 pages
File Size : 41,5 Mb
Release : 2021-10-27
Category : Mathematics
ISBN : 9783030890322

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Topological, Differential and Conformal Geometry of Surfaces by Norbert A'Campo Pdf

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.

Author : Jun O'Hara
Publisher : World Scientific
Page : 308 pages
File Size : 49,9 Mb
Release : 2003
Category : Mathematics
ISBN : 9812795308

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Energy of Knots and Conformal Geometry by Jun O'Hara Pdf

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."

Author : Francis E. Burstall,Dirk Ferus,Katrin Leschke,Franz Pedit,Ulrich Pinkall
Publisher : Springer
Page : 96 pages
File Size : 44,6 Mb
Release : 2004-10-20
Category : Mathematics
ISBN : 9783540453017

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Conformal Geometry of Surfaces in S4 and Quaternions by Francis E. Burstall,Dirk Ferus,Katrin Leschke,Franz Pedit,Ulrich Pinkall Pdf

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 : Pierre Anglès
Publisher : Springer Science & Business Media
Page : 307 pages
File Size : 53,5 Mb
Release : 2007-10-16
Category : Mathematics
ISBN : 9780817646431

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Conformal Groups in Geometry and Spin Structures by Pierre Anglès Pdf

This book provides a self-contained overview of the role of conformal groups in geometry and mathematical physics. It features a careful development of the material, from the basics of Clifford algebras to more advanced topics. Each chapter covers a specific aspect of conformal groups and conformal spin geometry. All major concepts are introduced and followed by detailed descriptions and definitions, and a comprehensive bibliography and index round out the work. Rich in exercises that are accompanied by full proofs and many hints, the book will be ideal as a course text or self-study volume for senior undergraduates and graduate students.

Author : Yi-Zhi Huang
Publisher : Springer Science & Business Media
Page : 289 pages
File Size : 40,8 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781461242765

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Two-Dimensional Conformal Geometry and Vertex Operator Algebras by Yi-Zhi Huang Pdf

The theory of vertex operator algebras and their representations has been showing its power in the solution of concrete mathematical problems and in the understanding of conceptual but subtle mathematical and physical struc- tures of conformal field theories. Much of the recent progress has deep connec- tions with complex analysis and conformal geometry. Future developments, especially constructions and studies of higher-genus theories, will need a solid geometric theory of vertex operator algebras. Back in 1986, Manin already observed in Man) that the quantum theory of (super )strings existed (in some sense) in two entirely different mathematical fields. Under canonical quantization this theory appeared to a mathematician as the representation theories of the Heisenberg, Vir as oro and affine Kac- Moody algebras and their superextensions. Quantization with the help of the Polyakov path integral led on the other hand to the analytic theory of algebraic (super ) curves and their moduli spaces, to invariants of the type of the analytic curvature, and so on.He pointed out further that establishing direct mathematical connections between these two forms of a single theory was a big and important problem. On the one hand, the theory of vertex operator algebras and their repre- sentations unifies (and considerably extends) the representation theories of the Heisenberg, Virasoro and Kac-Moody algebras and their superextensions.

Author : Miao Jin,Xianfeng Gu,Ying He,Yalin Wang
Publisher : Springer
Page : 314 pages
File Size : 53,9 Mb
Release : 2018-04-10
Category : Computers
ISBN : 9783319753324

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Conformal Geometry by Miao Jin,Xianfeng Gu,Ying He,Yalin Wang Pdf

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 : Xianfeng David Gu,Shing-Tung Yau
Publisher : Unknown
Page : 324 pages
File Size : 40,7 Mb
Release : 2008
Category : CD-ROMs
ISBN : UOM:39015080827697

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Computational Conformal Geometry by Xianfeng David Gu,Shing-Tung Yau Pdf

Author : Boris N. Apanasov
Publisher : Walter de Gruyter
Page : 541 pages
File Size : 54,6 Mb
Release : 2011-06-24
Category : Mathematics
ISBN : 9783110808056

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Conformal Geometry of Discrete Groups and Manifolds by Boris N. Apanasov Pdf

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)

Author : A. Rod Gover,Emanuele Latini,Andrew Waldron
Publisher : American Mathematical Soc.
Page : 85 pages
File Size : 51,7 Mb
Release : 2015-04-09
Category : Mathematics
ISBN : 9781470410926

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Poincare-Einstein Holography for Forms via Conformal Geometry in the Bulk by A. Rod Gover,Emanuele Latini,Andrew Waldron Pdf

The authors study higher form Proca equations on Einstein manifolds with boundary data along conformal infinity. They solve these Laplace-type boundary problems formally, and to all orders, by constructing an operator which projects arbitrary forms to solutions. They also develop a product formula for solving these asymptotic problems in general. The central tools of their approach are (i) the conformal geometry of differential forms and the associated exterior tractor calculus, and (ii) a generalised notion of scale which encodes the connection between the underlying geometry and its boundary. The latter also controls the breaking of conformal invariance in a very strict way by coupling conformally invariant equations to the scale tractor associated with the generalised scale.

Author : Abbas Bahri,Yongzhong Xu
Publisher : Imperial College Press
Page : 522 pages
File Size : 45,8 Mb
Release : 2007
Category : Mathematics
ISBN : 9781860948602

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Recent Progress in Conformal Geometry by Abbas Bahri,Yongzhong Xu Pdf

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
Publisher : Courier Dover Publications
Page : 308 pages
File Size : 52,9 Mb
Release : 2016-02-17
Category : Mathematics
ISBN : 9780486793443

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The Theory and Practice of Conformal Geometry by Steven G. Krantz Pdf

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.

Author : Sorin Dragomir,Liuiu Ornea
Publisher : Springer Science & Business Media
Page : 332 pages
File Size : 41,6 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781461220268

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Locally Conformal Kähler Geometry by Sorin Dragomir,Liuiu Ornea Pdf

. 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 : Steven G. Krantz
Publisher : Courier Dover Publications
Page : 304 pages
File Size : 51,8 Mb
Release : 2016-03-17
Category : Mathematics
ISBN : 9780486810324

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The Theory and Practice of Conformal Geometry by Steven G. Krantz Pdf

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 : Ravi S. Kulkarni
Publisher : Springer-Verlag
Page : 245 pages
File Size : 44,8 Mb
Release : 2013-03-09
Category : Mathematics
ISBN : 9783322906168

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Conformal Geometry by Ravi S. Kulkarni Pdf