The Theory And Practice Of Conformal Geometry

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The Theory and Practice of Conformal Geometry

Author : Steven G. Krantz
Publisher : Courier Dover Publications
ISBN 13 : 0486810321
Total Pages : 304 pages
Book Rating : 4.4/5 (868 download)

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Book Synopsis The Theory and Practice of Conformal Geometry by : Steven G. Krantz

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.

Conformal Geometry of Surfaces in S4 and Quaternions

Author : Francis E. Burstall
Publisher : Springer
ISBN 13 : 3540453016
Total Pages : 96 pages
Book Rating : 4.5/5 (44 download)

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Book Synopsis Conformal Geometry of Surfaces in S4 and Quaternions by : Francis E. Burstall

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.

Conformal Maps And Geometry

Author : Dmitry Beliaev
Publisher : World Scientific
ISBN 13 : 178634615X
Total Pages : 240 pages
Book Rating : 4.7/5 (863 download)

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Book Synopsis Conformal Maps And Geometry by : Dmitry Beliaev

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.

Energy of Knots and Conformal Geometry

Author : Jun O'Hara
Publisher : World Scientific
ISBN 13 : 981448640X
Total Pages : 304 pages
Book Rating : 4.8/5 (144 download)

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Book Synopsis Energy of Knots and Conformal Geometry by : Jun O'Hara

Download or read book Energy of Knots and Conformal Geometry written by Jun O'Hara and published by World Scientific. This book was released on 2003-03-25 with total page 304 pages. Available in PDF, EPUB and Kindle. Book excerpt: Energy of knots is a theory that was introduced to create a “canonical configuration” of a knot — 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 “canonical configuration” 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 “Optimal Embedding” of a Knot:α-Energy Functional E(α)On E(2)Lp Norm Energy with Higher IndexNumerical ExperimentsStereo Pictures of E(2)MinimizersEnergy of Knots in a Riemannian ManifoldPhysical Knot EnergiesEnergy of Knots from a Conformal Geometric Viewpoint:Preparation from Conformal GeometryThe Space of Non-Trivial Spheres of a KnotThe Infinitesimal Cross RatioThe Conformal Sin Energy Esin θMeasure of Non-Trivial SpheresAppendices:Generalization of the Gauss Formula for the Linking NumberThe 3-Tuple Map to the Set of Circles in S3Conformal Moduli of a Solid TorusKirchhoff ElasticaOpen Problems and Dreams Readership: Graduate students and researchers in geometry & topology and numerical & computational mathematics. Keywords:Energy of Knots;Optimal Embedding;Conformal Geometry;MÃ¶bius Transformation;Infinitesimal Cross RatioReviews:“… this book gives an excellent, state of the art account of many of the important results in this field. A strong point of the book is that almost all proofs of the theorems stated are included.”Zentralblatt MATH

Computational Conformal Geometry

Author : Xianfeng David Gu
Publisher :
ISBN 13 :
Total Pages : 324 pages
Book Rating : 4.3/5 (91 download)

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Book Synopsis Computational Conformal Geometry by : Xianfeng David Gu

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:

Conformal Geometry

Author : Ravi S. Kulkarni
Publisher : Vieweg+teubner Verlag
ISBN 13 :
Total Pages : 256 pages
Book Rating : 4.3/5 (91 download)

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Book Synopsis Conformal Geometry by : Ravi S. Kulkarni

Download or read book Conformal Geometry written by Ravi S. Kulkarni and published by Vieweg+teubner Verlag. This book was released on 1988 with total page 256 pages. Available in PDF, EPUB and Kindle. Book excerpt: The contributions in this volume summarize parts of a seminar on conformal geometry which was held at the Max-Planck-Institut fur Mathematik in Bonn during the academic year 1985/86. The intention of this seminar was to study conformal structures on mani folds from various viewpoints. The motivation to publish seminar notes grew out of the fact that in spite of the basic importance of this field to many topics of current interest (low-dimensional topology, analysis on manifolds . . . ) there seems to be no coherent introduction to conformal geometry in the literature. We have tried to make the material presented in this book self-contained, so it should be accessible to students with some background in differential geometry. Moreover, we hope that it will be useful as a reference and as a source of inspiration for further research. Ravi Kulkarni/Ulrich Pinkall Conformal Structures and Mobius Structures Ravi S. Kulkarni* Contents § 0 Introduction 2 § 1 Conformal Structures 4 § 2 Conformal Change of a Metric, Mobius Structures 8 § 3 Liouville's Theorem 12 n §4 The GroupsM(n) andM(E ) 13 § 5 Connection with Hyperbol ic Geometry 16 § 6 Constructions of Mobius Manifolds 21 § 7 Development and Holonomy 31 § 8 Ideal Boundary, Classification of Mobius Structures 35 * Partially supported by the Max-Planck-Institut fur Mathematik, Bonn, and an NSF grant. 2 §O Introduction (0. 1) Historically, the stereographic projection and the Mercator projection must have appeared to mathematicians very startling.

Conformal Differential Geometry and Its Generalizations

Author : Maks A. Akivis
Publisher : John Wiley & Sons
ISBN 13 : 1118030885
Total Pages : 404 pages
Book Rating : 4.1/5 (18 download)

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Book Synopsis Conformal Differential Geometry and Its Generalizations by : Maks A. Akivis

Download or read book Conformal Differential Geometry and Its Generalizations written by Maks A. Akivis and published by John Wiley & Sons. This book was released on 2011-09-20 with total page 404 pages. Available in PDF, EPUB and Kindle. Book excerpt: Comprehensive coverage of the foundations, applications, recent developments, and future of conformal differential geometry Conformal Differential Geometry and Its Generalizations is the first and only text that systematically presents the foundations and manifestations of conformal differential geometry. It offers the first unified presentation of the subject, which was established more than a century ago. The text is divided into seven chapters, each containing figures, formulas, and historical and bibliographical notes, while numerous examples elucidate the necessary theory. Clear, focused, and expertly synthesized, Conformal Differential Geometry and Its Generalizations * Develops the theory of hypersurfaces and submanifolds of any dimension of conformal and pseudoconformal spaces. * Investigates conformal and pseudoconformal structures on a manifold of arbitrary dimension, derives their structure equations, and explores their tensor of conformal curvature. * Analyzes the real theory of four-dimensional conformal structures of all possible signatures. * Considers the analytic and differential geometry of Grassmann and almost Grassmann structures. * Draws connections between almost Grassmann structures and web theory. Conformal differential geometry, a part of classical differential geometry, was founded at the turn of the century and gave rise to the study of conformal and almost Grassmann structures in later years. Until now, no book has offered a systematic presentation of the multidimensional conformal differential geometry and the conformal and almost Grassmann structures. After years of intense research at their respective universities and at the Soviet School of Differential Geometry, Maks A. Akivis and Vladislav V. Goldberg have written this well-conceived, expertly executed volume to fill a void in the literature. Dr. Akivis and Dr. Goldberg supply a deep foundation, applications, numerous examples, and recent developments in the field. Many of the findings that fill these pages are published here for the first time, and previously published results are reexamined in a unified context. The geometry and theory of conformal and pseudoconformal spaces of arbitrary dimension, as well as the theory of Grassmann and almost Grassmann structures, are discussed and analyzed in detail. The topics covered not only advance the subject itself, but pose important questions for future investigations. This exhaustive, groundbreaking text combines the classical results and recent developments and findings. This volume is intended for graduate students and researchers of differential geometry. It can be especially useful to those students and researchers who are interested in conformal and Grassmann differential geometry and their applications to theoretical physics.

Conformal Geometry of Surfaces in S4 and Quaternions

Author :
Publisher :
ISBN 13 :
Total Pages : 74 pages
Book Rating : 4.:/5 (54 download)

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Book Synopsis Conformal Geometry of Surfaces in S4 and Quaternions by :

Download or read book Conformal Geometry of Surfaces in S4 and Quaternions written by and published by . This book was released on 2000 with total page 74 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Conformal Geometry

Author : Miao Jin
Publisher : Springer
ISBN 13 : 3319753320
Total Pages : 314 pages
Book Rating : 4.3/5 (197 download)

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Book Synopsis Conformal Geometry by : Miao Jin

Download or read book Conformal Geometry written by Miao Jin and published by Springer. This book was released on 2018-04-10 with total page 314 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Inversion Theory and Conformal Mapping

Author : David E. Blair
Publisher : American Mathematical Soc.
ISBN 13 : 0821826360
Total Pages : 130 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Inversion Theory and Conformal Mapping by : David E. Blair

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.

Conformal Dimension

Author : John M. Mackay
Publisher : American Mathematical Soc.
ISBN 13 : 0821852299
Total Pages : 162 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Conformal Dimension by : John M. Mackay

Download or read book Conformal Dimension written by John M. Mackay and published by American Mathematical Soc.. This book was released on 2010 with total page 162 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Recent Progress in Conformal Geometry

Author : Abbas Bahri
Publisher : World Scientific
ISBN 13 : 1860947727
Total Pages : 522 pages
Book Rating : 4.8/5 (69 download)

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Book Synopsis Recent Progress in Conformal Geometry by : Abbas Bahri

Download or read book Recent Progress in Conformal Geometry written by Abbas Bahri and published by World Scientific. This book was released on 2007 with total page 522 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Function Spaces in Analysis

Author : Krzysztof Jarosz
Publisher : American Mathematical Soc.
ISBN 13 : 1470416948
Total Pages : 301 pages
Book Rating : 4.4/5 (74 download)

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Book Synopsis Function Spaces in Analysis by : Krzysztof Jarosz

Download or read book Function Spaces in Analysis written by Krzysztof Jarosz and published by American Mathematical Soc.. This book was released on 2015-07-28 with total page 301 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains the proceedings of the Seventh Conference on Function Spaces, which was held from May 20-24, 2014 at Southern Illinois University at Edwardsville. The papers cover a broad range of topics, including spaces and algebras of analytic functions of one and of many variables (and operators on such spaces), spaces of integrable functions, spaces of Banach-valued functions, isometries of function spaces, geometry of Banach spaces, and other related subjects.

Prescribing Scalar Curvature in Conformal Geometry

Author : Andrea Malchiodi
Publisher :
ISBN 13 : 9783985470525
Total Pages : 0 pages
Book Rating : 4.4/5 (75 download)

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Book Synopsis Prescribing Scalar Curvature in Conformal Geometry by : Andrea Malchiodi

Download or read book Prescribing Scalar Curvature in Conformal Geometry written by Andrea Malchiodi and published by . This book was released on 2023 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Conformal Mapping

Author : Zeev Nehari
Publisher : Courier Corporation
ISBN 13 : 0486145034
Total Pages : 418 pages
Book Rating : 4.4/5 (861 download)

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Book Synopsis Conformal Mapping by : Zeev Nehari

Download or read book Conformal Mapping written by Zeev Nehari and published by Courier Corporation. This book was released on 2012-05-23 with total page 418 pages. Available in PDF, EPUB and Kindle. Book excerpt: Conformal mapping is a field in which pure and applied mathematics are both involved. This book tries to bridge the gulf that many times divides these two disciplines by combining the theoretical and practical approaches to the subject. It will interest the pure mathematician, engineer, physicist, and applied mathematician. The potential theory and complex function theory necessary for a full treatment of conformal mapping are developed in the first four chapters, so the reader needs no other text on complex variables. These chapters cover harmonic functions, analytic functions, the complex integral calculus, and families of analytic functions. Included here are discussions of Green's formula, the Poisson formula, the Cauchy-Riemann equations, Cauchy's theorem, the Laurent series, and the Residue theorem. The final three chapters consider in detail conformal mapping of simply-connected domains, mapping properties of special functions, and conformal mapping of multiply-connected domains. The coverage here includes such topics as the Schwarz lemma, the Riemann mapping theorem, the Schwarz-Christoffel formula, univalent functions, the kernel function, elliptic functions, univalent functions, the kernel function, elliptic functions, the Schwarzian s-functions, canonical domains, and bounded functions. There are many problems and exercises, making the book useful for both self-study and classroom use. The author, former professor of mathematics at Carnegie-Mellon University, has designed the book as a semester's introduction to functions of a complex variable followed by a one-year graduate course in conformal mapping. The material is presented simply and clearly, and the only prerequisite is a good working knowledge of advanced calculus.

Fifth International Congress of Chinese Mathematicians

Author : Lizhen Ji
Publisher : American Mathematical Soc.
ISBN 13 : 0821875876
Total Pages : 522 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Fifth International Congress of Chinese Mathematicians by : Lizhen Ji

Download or read book Fifth International Congress of Chinese Mathematicians written by Lizhen Ji and published by American Mathematical Soc.. This book was released on 2012 with total page 522 pages. Available in PDF, EPUB and Kindle. Book excerpt: This two-part volume represents the proceedings of the Fifth International Congress of Chinese Mathematicians, held at Tsinghua University, Beijing, in December 2010. The Congress brought together eminent Chinese and overseas mathematicians to discuss the latest developments in pure and applied mathematics. Included are 60 papers based on lectures given at the conference.

Uniformizing Dessins and BelyiMaps via Circle Packing

Author : Philip L. Bowers
Publisher : American Mathematical Soc.
ISBN 13 : 0821835238
Total Pages : 118 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Uniformizing Dessins and BelyiMaps via Circle Packing by : Philip L. Bowers

Download or read book Uniformizing Dessins and BelyiMaps via Circle Packing written by Philip L. Bowers and published by American Mathematical Soc.. This book was released on 2004 with total page 118 pages. Available in PDF, EPUB and Kindle. Book excerpt: Introduction Dessins d'enfants Discrete Dessins via circle packing Uniformizing Dessins A menagerie of Dessins d'enfants Computational issues Additional constructions Non-equilateral triangulations The discrete option Appendix: Implementation Bibliography.