Geometry Of Harmonic Maps

Author : Yuanlong Xin
Publisher : Springer Science & Business Media
Page : 252 pages
File Size : 55,8 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781461240846

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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,Luc Lemaire
Publisher : World Scientific
Page : 38 pages
File Size : 54,7 Mb
Release : 1995
Category : Mathematics
ISBN : 9810214669

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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, å-models in physics. Recently, they have become powerful tools in the study of global properties of Riemannian and K„hlerian 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.

Author : Eric Loubeau,Stefano Montaldo
Publisher : American Mathematical Soc.
Page : 296 pages
File Size : 47,7 Mb
Release : 2011
Category : Geometry, Differential
ISBN : 9780821849873

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Harmonic Maps and Differential Geometry by Eric Loubeau,Stefano Montaldo Pdf

This volume contains the proceedings of a conference held in Cagliari, Italy, from September 7-10, 2009, to celebrate John C. Wood's 60th birthday. These papers reflect the many facets of the theory of harmonic maps and its links and connections with other topics in Differential and Riemannian Geometry. Two long reports, one on constant mean curvature surfaces by F. Pedit and the other on the construction of harmonic maps by J. C. Wood, open the proceedings. These are followed by a mix of surveys on Prof. Wood's area of expertise: Lagrangian surfaces, biharmonic maps, locally conformally Kahler manifolds and the DDVV conjecture, as well as several research papers on harmonic maps. Other research papers in the volume are devoted to Willmore surfaces, Goldstein-Pedrich flows, contact pairs, prescribed Ricci curvature, conformal fibrations, the Fadeev-Hopf model, the Compact Support Principle and the curvature of surfaces.

Author : Jürgen Jost
Publisher : Springer
Page : 143 pages
File Size : 42,5 Mb
Release : 2006-12-08
Category : Mathematics
ISBN : 9783540388685

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Harmonic Maps Between Surfaces by Jürgen Jost Pdf

Author : Richard M. Schoen,Shing-Tung Yau
Publisher : International Press of Boston
Page : 414 pages
File Size : 45,8 Mb
Release : 1997
Category : Mathematics
ISBN : UOM:39015040999677

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Lectures on Harmonic Maps by Richard M. Schoen,Shing-Tung Yau Pdf

A presentation of research on harmonic maps, based on lectures given at the University of California, San Diego. Schoen has worked to use the Fells/Sampson theorem to reprove the rigidity theorem of Masfow and superrigidity theorem of Marqulis. Many of these developments are recorded here.

Author : Christopher Kum Anand,Paul Baird,John Colin Wood,Eric Loubeau
Publisher : CRC Press
Page : 332 pages
File Size : 47,6 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 : John C. Wood
Publisher : Springer-Verlag
Page : 328 pages
File Size : 51,9 Mb
Release : 2013-07-02
Category : Mathematics
ISBN : 9783663140924

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Harmonic Maps and Integrable Systems by John C. Wood Pdf

Author : James Eells,Luc Lemaire
Publisher : American Mathematical Soc.
Page : 108 pages
File Size : 41,5 Mb
Release : 1983-01-01
Category : Mathematics
ISBN : 0821888951

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Selected Topics in Harmonic Maps by James Eells,Luc Lemaire Pdf

Author : James Eells
Publisher : World Scientific
Page : 472 pages
File Size : 53,5 Mb
Release : 1992
Category : Mathematics
ISBN : 9810207042

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Harmonic Maps by James Eells Pdf

These original research papers, written during a period of over a quarter of a century, have two main objectives. The first is to lay the foundations of the theory of harmonic maps between Riemannian Manifolds, and the second to establish various existence and regularity theorems as well as the explicit constructions of such maps.

Author : James Eells
Publisher : World Scientific
Page : 452 pages
File Size : 52,5 Mb
Release : 1992-08-21
Category : Science
ISBN : 9789814506120

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Harmonic Maps by James Eells Pdf

These original research papers, written during a period of over a quarter of a century, have two main objectives. The first is to lay the foundations of the theory of harmonic maps between Riemannian Manifolds, and the second to establish various existence and regularity theorems as well as the explicit constructions of such maps. Contents:Harmonic Mappings of Riemannian Manifolds (1964)Énergie et Déformations en Géométrie Différentielle (1964)Variational Theory in Fibre Bundles (1965)Restrictions on Harmonic Maps of Surfaces (1976)The Surfaces of Delaunay (1987)Minimal Graphs (1979)On the Construction of Harmonic and Holomorphic Maps between Surfaces (1980)Deformations of Metrics and Associated Harmonic Maps (1981)A Conservation Law for Harmonic Maps (1981)Maps of Minimum Energy (1981)The Existence and Construction of Certain Harmonic Maps (1982)Harmonic Maps from Surfaces to Complex Projective Spaces (1983)Examples of Harmonic Maps from Disks to Hemispheres (1984)Variational Theory in Fibre Bundles: Examples (1983)Constructions Twistorielles des Applications Harmoniques (1983)Removable Singularities of Harmonic Maps (1984)On Equivariant Harmonic Maps (1984)Regularity of Certain Harmonic Maps (1984)Gauss Maps of Surfaces (1984)Minimal Branched Immersions into Three-Manifolds (1985)Twistorial Construction of Harmonic Maps of Surfaces into Four-Manifolds (1985)Certain Variational Principles in Riemannian Geometry (1985)Harmonic Maps and Minimal Surface Coboundaries (1987)Unstable Minimal Surface Coboundaries (1986)Harmonic Maps between Spheres and Ellipsoids (1990)On Representing Homotopy Classes by Harmonic Maps (1991) Readership: Researchers and students in differential geometry and topology and theoretical physicists. keywords:Harmonic Mapping;Energy;Holomorphic Map;First (Second) Variation of Energy;Minimal Immersion;Minimal Graph;Regularity of Maps;Removable Singularities“It is striking that the papers cut a wide swathe through mathematics, and this is a testimony to the fact that the author has influenced so many younger mathematicians, several of whom are represented here.”Mathematical Reviews

Author : James Eells,Andrea Ratto
Publisher : Princeton University Press
Page : 240 pages
File Size : 41,6 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 : James Eells,Andrea Ratto
Publisher : Princeton University Press
Page : 238 pages
File Size : 43,5 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 : Martin A. Guest
Publisher : Cambridge University Press
Page : 202 pages
File Size : 45,8 Mb
Release : 1997-01-13
Category : Mathematics
ISBN : 0521589320

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Harmonic Maps, Loop Groups, and Integrable Systems by Martin A. Guest Pdf

Harmonic maps are generalisations of the concept of geodesics. They encompass many fundamental examples in differential geometry and have recently become of widespread use in many areas of mathematics and mathematical physics. This is an accessible introduction to some of the fundamental connections between differential geometry, Lie groups, and integrable Hamiltonian systems. The specific goal of the book is to show how the theory of loop groups can be used to study harmonic maps. By concentrating on the main ideas and examples, the author leads up to topics of current research. The book is suitable for students who are beginning to study manifolds and Lie groups, and should be of interest both to mathematicians and to theoretical physicists.

Author : Malcolm Black
Publisher : Routledge
Page : 104 pages
File Size : 49,5 Mb
Release : 2018-05-04
Category : Mathematics
ISBN : 9781351441629

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Harmonic Maps Into Homogeneous Spaces by Malcolm Black Pdf

Harmonic maps and the related theory of minimal surfaces are variational problems of long standing in differential geometry. Many important advances have been made in understanding harmonic maps of Riemann surfaces into symmetric spaces. In particular, ""twistor methods"" construct some, and in certain cases all, such mappings from holomorphic data. These notes develop techniques applicable to more general homogeneous manifolds, in particular a very general twistor result is proved. When applied to flag manifolds, this wider viewpoint allows many of the previously unrelated twistor results for symmetric spaces to be brought into a unified framework. These methods also enable a classification of harmonic maps into full flag manifolds to be established, and new examples are constructed. The techniques used are mostly a blend of the theory of compact Lie groups and complex differential geometry. This book should be of interest to mathematicians with experience in differential geometry and to theoretical physicists.

Author : James Eells,B. Fuglede
Publisher : Cambridge University Press
Page : 316 pages
File Size : 52,9 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.