Harmonic Maps And Minimal Immersions With Symmetries

Author : James Eells,Andrea Ratto
Publisher : Princeton University Press
Page : 238 pages
File Size : 54,5 Mb
Release : 1993
Category : Mathematics
ISBN : 069110249X

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Harmonic Maps and Minimal Immersions with Symmetries by James Eells,Andrea Ratto Pdf

The aim of this book is to study harmonic maps, minimal and parallel mean curvature immersions in the presence of symmetry. In several instances, the latter permits reduction of the original elliptic variational problem to the qualitative study of certain ordinary differential equations: the authors' primary objective is to provide representative examples to illustrate these reduction methods and their associated analysis with geometric and topological applications. The material covered by the book displays a solid interplay involving geometry, analysis and topology: in particular, it includes a basic presentation of 1-cohomogeneous equivariant differential geometry and of the theory of harmonic maps between spheres.

Author : James Eells,Andrea Ratto
Publisher : Princeton University Press
Page : 240 pages
File Size : 49,7 Mb
Release : 2016-03-02
Category : Mathematics
ISBN : 9781400882502

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Harmonic Maps and Minimal Immersions with Symmetries (AM-130), Volume 130 by James Eells,Andrea Ratto Pdf

The aim of this book is to study harmonic maps, minimal and parallel mean curvature immersions in the presence of symmetry. In several instances, the latter permits reduction of the original elliptic variational problem to the qualitative study of certain ordinary differential equations: the authors' primary objective is to provide representative examples to illustrate these reduction methods and their associated analysis with geometric and topological applications. The material covered by the book displays a solid interplay involving geometry, analysis and topology: in particular, it includes a basic presentation of 1-cohomogeneous equivariant differential geometry and of the theory of harmonic maps between spheres.

Author : Gábor Tóth (Ph. D.)
Publisher : Unknown
Page : 176 pages
File Size : 44,5 Mb
Release : 1990
Category : Mathematics
ISBN : UOM:39015018970650

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Harmonic Maps and Minimal Immersions Through Representation Theory by Gábor Tóth (Ph. D.) Pdf

Author : James Eells,Luc Lemaire
Publisher : World Scientific
Page : 228 pages
File Size : 53,7 Mb
Release : 1995-03-29
Category : Mathematics
ISBN : 9789814502924

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Two Reports on Harmonic Maps by James Eells,Luc Lemaire Pdf

Harmonic maps between Riemannian manifolds are solutions of systems of nonlinear partial differential equations which appear in different contexts of differential geometry. They include holomorphic maps, minimal surfaces, σ-models in physics. Recently, they have become powerful tools in the study of global properties of Riemannian and Kählerian manifolds. A standard reference for this subject is a pair of Reports, published in 1978 and 1988 by James Eells and Luc Lemaire. This book presents these two reports in a single volume with a brief supplement reporting on some recent developments in the theory. It is both an introduction to the subject and a unique source of references, providing an organized exposition of results spread throughout more than 800 papers. Contents:IntroductionOperations on Vector BundlesHarmonic MapsComposition PropertiesMaps into Manifolds of Nonpositive (≤ 0) CurvatureThe Existence Theorem for Riem N ≤ 0Maps into Flat ManifoldsHarmonic Maps between SpheresHolomorphic MapsHarmonic Maps of a SurfaceHarmonic Maps between SurfacesHarmonic Maps of Manifolds with Boundary Readership: Mathematicians and mathematical physicists. keywords:Harmonic Maps;Minimal Immersions;Totally Geodesic Maps;Kaehler Manifold;(1,1)-Geodesic Map;Dilatation;Nonpositive Sectional Curvature;Holomorphic Map;Teichmueller Map;Twistor Construction “… an interesting account of the progress made in the theory of harmonic maps until the year 1988 … this master-piece work will serve as an influence and good reference in the very active subject of harmonic maps both from the points of view of theory and applications.” Mathematics Abstracts

Author : Gabor Toth
Publisher : Springer Science & Business Media
Page : 332 pages
File Size : 43,7 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781461300618

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Finite Möbius Groups, Minimal Immersions of Spheres, and Moduli by Gabor Toth Pdf

"Spherical soap bubbles", isometric minimal immersions of round spheres into round spheres, or spherical immersions for short, belong to a fast growing and fascinating area between algebra and geometry. In this accessible book, the author traces the development of the study of spherical minimal immersions over the past 30 plus years, including a valuable selection of exercises.

Author : Christopher Kum Anand,Paul Baird,John Colin Wood,Eric Loubeau
Publisher : CRC Press
Page : 332 pages
File Size : 52,8 Mb
Release : 1999-10-13
Category : Mathematics
ISBN : 1584880325

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Harmonic Morphisms, Harmonic Maps and Related Topics by Christopher Kum Anand,Paul Baird,John Colin Wood,Eric Loubeau Pdf

The subject of harmonic morphisms is relatively new but has attracted a huge worldwide following. Mathematicians, young researchers and distinguished experts came from all corners of the globe to the City of Brest - site of the first, international conference devoted to the fledgling but dynamic field of harmonic morphisms. Harmonic Morphisms, Harmonic Maps, and Related Topics reports the proceedings of that conference, forms the first work primarily devoted to harmonic morphisms, bringing together contributions from the founders of the subject, leading specialists, and experts in other related fields. Starting with "The Beginnings of Harmonic Morphisms," which provides the essential background, the first section includes papers on the stability of harmonic morphisms, global properties, harmonic polynomial morphisms, Bochner technique, f-structures, symplectic harmonic morphisms, and discrete harmonic morphisms. The second section addresses the wider domain of harmonic maps and contains some of the most recent results on harmonic maps and surfaces. The final section highlights the rapidly developing subject of constant mean curvature surfaces. Harmonic Morphisms, Harmonic Maps, and Related Topics offers a coherent, balanced account of this fast-growing subject that furnishes a vital reference for anyone working in the field.

Author : Yuan-Jen Chiang
Publisher : Springer Science & Business Media
Page : 418 pages
File Size : 41,7 Mb
Release : 2013-06-18
Category : Mathematics
ISBN : 9783034805346

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Developments of Harmonic Maps, Wave Maps and Yang-Mills Fields into Biharmonic Maps, Biwave Maps and Bi-Yang-Mills Fields by Yuan-Jen Chiang Pdf

Harmonic maps between Riemannian manifolds were first established by James Eells and Joseph H. Sampson in 1964. Wave maps are harmonic maps on Minkowski spaces and have been studied since the 1990s. Yang-Mills fields, the critical points of Yang-Mills functionals of connections whose curvature tensors are harmonic, were explored by a few physicists in the 1950s, and biharmonic maps (generalizing harmonic maps) were introduced by Guoying Jiang in 1986. The book presents an overview of the important developments made in these fields since they first came up. Furthermore, it introduces biwave maps (generalizing wave maps) which were first studied by the author in 2009, and bi-Yang-Mills fields (generalizing Yang-Mills fields) first investigated by Toshiyuki Ichiyama, Jun-Ichi Inoguchi and Hajime Urakawa in 2008. Other topics discussed are exponential harmonic maps, exponential wave maps and exponential Yang-Mills fields.

Author : Yuanlong Xin
Publisher : Springer Science & Business Media
Page : 264 pages
File Size : 46,6 Mb
Release : 1996-04-30
Category : Mathematics
ISBN : 0817638202

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Geometry of Harmonic Maps by Yuanlong Xin Pdf

Harmonic maps are solutions to a natural geometrical variational prob lem. This notion grew out of essential notions in differential geometry, such as geodesics, minimal surfaces and harmonic functions. Harmonic maps are also closely related to holomorphic maps in several complex variables, to the theory of stochastic processes, to nonlinear field theory in theoretical physics, and to the theory of liquid crystals in materials science. During the past thirty years this subject has been developed extensively. The monograph is by no means intended to give a complete description of the theory of harmonic maps. For example, the book excludes a large part of the theory of harmonic maps from 2-dimensional domains, where the methods are quite different from those discussed here. The first chapter consists of introductory material. Several equivalent definitions of harmonic maps are described, and interesting examples are presented. Various important properties and formulas are derived. Among them are Bochner-type formula for the energy density and the second varia tional formula. This chapter serves not only as a basis for the later chapters, but also as a brief introduction to the theory. Chapter 2 is devoted to the conservation law of harmonic maps. Em phasis is placed on applications of conservation law to the mono tonicity formula and Liouville-type theorems.

Author : James Eells,B. Fuglede
Publisher : Cambridge University Press
Page : 316 pages
File Size : 44,6 Mb
Release : 2001-07-30
Category : Mathematics
ISBN : 0521773113

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Harmonic Maps Between Riemannian Polyhedra by James Eells,B. Fuglede Pdf

A research level book on harmonic maps between singular spaces, by renowned authors, first published in 2001.

Author : Sorin Dragomir,Domenico Perrone
Publisher : Elsevier
Page : 529 pages
File Size : 52,9 Mb
Release : 2011-10-26
Category : Computers
ISBN : 9780124158269

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Harmonic Vector Fields by Sorin Dragomir,Domenico Perrone Pdf

An excellent reference for anyone needing to examine properties of harmonic vector fields to help them solve research problems. The book provides the main results of harmonic vector ?elds with an emphasis on Riemannian manifolds using past and existing problems to assist you in analyzing and furnishing your own conclusion for further research. It emphasizes a combination of theoretical development with practical applications for a solid treatment of the subject useful to those new to research using differential geometric methods in extensive detail. A useful tool for any scientist conducting research in the field of harmonic analysis Provides applications and modern techniques to problem solving A clear and concise exposition of differential geometry of harmonic vector fields on Reimannian manifolds Physical Applications of Geometric Methods

Author : Marcel Berger
Publisher : Springer Science & Business Media
Page : 824 pages
File Size : 49,7 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9783642182457

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A Panoramic View of Riemannian Geometry by Marcel Berger Pdf

This book introduces readers to the living topics of Riemannian Geometry and details the main results known to date. The results are stated without detailed proofs but the main ideas involved are described, affording the reader a sweeping panoramic view of almost the entirety of the field. From the reviews "The book has intrinsic value for a student as well as for an experienced geometer. Additionally, it is really a compendium in Riemannian Geometry." --MATHEMATICAL REVIEWS

Author : Maria Falcitelli,Anna Maria Pastore,Stere Ianus?
Publisher : World Scientific
Page : 292 pages
File Size : 55,6 Mb
Release : 2004
Category : Mathematics
ISBN : 9789812562333

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Riemannian Submersions and Related Topics by Maria Falcitelli,Anna Maria Pastore,Stere Ianus? Pdf

This book provides the first-ever systematic introduction to thetheory of Riemannian submersions, which was initiated by BarrettO''Neill and Alfred Gray less than four decades ago. The authorsfocus their attention on classification theorems when the total spaceand the fibres have nice geometric properties.

Author : Maria Falcitelli,Anna Maria Pastore,Stere Ianus
Publisher : World Scientific
Page : 292 pages
File Size : 53,9 Mb
Release : 2004-06-21
Category : Mathematics
ISBN : 9789814482455

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Riemannian Submersions and Related Topics by Maria Falcitelli,Anna Maria Pastore,Stere Ianus Pdf

' This book provides the first-ever systematic introduction to the theory of Riemannian submersions, which was initiated by Barrett O'Neill and Alfred Gray less than four decades ago. The authors focus their attention on classification theorems when the total space and the fibres have nice geometric properties. Particular emphasis is placed on the interrelation with almost Hermitian, almost contact and quaternionic geometry. Examples clarifying and motivating the theory are included in every chapter. Recent results on semi-Riemannian submersions are also explained. Finally, the authors point out the close connection of the subject with some areas of physics. Contents:Riemannian SubmersionsSubmersions with Totally Geodesic FibresAlmost Hermitian SubmersionsRiemannian Submersions and Contact Metric ManifoldsEinstein Spaces and Riemannian SubmersionsRiemannian Submersions and SubmanifoldsSemi-Riemannian SubmersionsApplications of Riemannian Submersions in Physics Readership: Graduate students and researchers in differential geometry, Riemannian geometry and related fields such as physics. Keywords:Riemannian Submersions;Almost Hermitian Geometry;Contact Metric Manifolds;Einstein Spaces;Semi-Riemannian SubmersionsKey Features:First systematic exposition devoted to Riemannian submersionsDeals with current materialContains a wide-ranging bibliography and about 350 referencesReviews:“The reader should have little difficulty in locating the many different concepts in this rich and rewarding text. Young geometers looking for problems and more importantly directions for future work will find reading this book provides a fine source of material and papers.”Mathematical Reviews “This is a very well-written and interesting book on Riemannian submersions and it is the first monograph in the literature about this topic.”Zentralblatt MATH “Well written, gathering information spread in a lot of papers, unifying the style of many authors, with most of the proofs carried in all details, with a wealth of examples, it certainly fills a gap in the literature and will be a prior reference for both researchers and students.”Romanian Journal of Pure and Applied Mathematics '

Author : Dennis Koh
Publisher : Universitätsverlag Potsdam
Page : 76 pages
File Size : 46,6 Mb
Release : 2008
Category : Electronic
ISBN : 9783940793249

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The Evolution Equation for Closed Magnetic Geodesics by Dennis Koh Pdf

Author : Mikhail Aleksandrovich Shubin,Maxim Braverman
Publisher : American Mathematical Soc.
Page : 223 pages
File Size : 49,9 Mb
Release : 2011-02-10
Category : Mathematics
ISBN : 9780821849484

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Spectral Theory and Geometric Analysis by Mikhail Aleksandrovich Shubin,Maxim Braverman Pdf

The papers in this volume cover important topics in spectral theory and geometric analysis such as resolutions of smooth group actions, spectral asymptotics, solutions of the Ginzburg-Landau equation, scattering theory, Riemann surfaces of infinite genus and tropical mathematics.