Two Reports On Harmonic Maps

Author : James Eells,Luc Lemaire
Publisher : World Scientific
Page : 38 pages
File Size : 49,6 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 : James Eells,Luc Lemaire
Publisher : World Scientific
Page : 228 pages
File Size : 40,5 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 : James Eells
Publisher : World Scientific
Page : 472 pages
File Size : 51,9 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 : 43,8 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 : Eric Loubeau,Stefano Montaldo
Publisher : American Mathematical Soc.
Page : 296 pages
File Size : 53,8 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 : James Eells,Luc Lemaire
Publisher : American Mathematical Soc.
Page : 108 pages
File Size : 51,5 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 : Yuanlong Xin
Publisher : Springer Science & Business Media
Page : 264 pages
File Size : 50,9 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 : Paul Baird,John C. Wood
Publisher : Oxford University Press
Page : 540 pages
File Size : 50,8 Mb
Release : 2003
Category : Mathematics
ISBN : 0198503628

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Harmonic Morphisms Between Riemannian Manifolds by Paul Baird,John C. Wood Pdf

This is an account in book form of the theory of harmonic morphisms between Riemannian manifolds.

Author : Jurgen Jost
Publisher : Unknown
Page : 154 pages
File Size : 53,8 Mb
Release : 2014-01-15
Category : Electronic
ISBN : 3662191679

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Harmonic Maps Between Surfaces by Jurgen Jost Pdf

Author : Chaohao Gu,Anning Hu,Zixiang Zhou
Publisher : Springer Science & Business Media
Page : 308 pages
File Size : 46,6 Mb
Release : 2006-07-09
Category : Science
ISBN : 9781402030888

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Darboux Transformations in Integrable Systems by Chaohao Gu,Anning Hu,Zixiang Zhou Pdf

The Darboux transformation approach is one of the most effective methods for constructing explicit solutions of partial differential equations which are called integrable systems and play important roles in mechanics, physics and differential geometry. This book presents the Darboux transformations in matrix form and provides purely algebraic algorithms for constructing the explicit solutions. A basis for using symbolic computations to obtain the explicit exact solutions for many integrable systems is established. Moreover, the behavior of simple and multi-solutions, even in multi-dimensional cases, can be elucidated clearly. The method covers a series of important equations such as various kinds of AKNS systems in R1+n, harmonic maps from 2-dimensional manifolds, self-dual Yang-Mills fields and the generalizations to higher dimensional case, theory of line congruences in three dimensions or higher dimensional space etc. All these cases are explained in detail. This book contains many results that were obtained by the authors in the past few years. Audience: The book has been written for specialists, teachers and graduate students (or undergraduate students of higher grade) in mathematics and physics.

Author : Paul Gauduchon
Publisher : World Scientific
Page : 390 pages
File Size : 42,5 Mb
Release : 1988-10-01
Category : Mathematics
ISBN : 9789813201484

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Harmonic Mappings, Twistors And Sigma Models by Paul Gauduchon Pdf

Harmonic mappings have played in recent years and will likely to play in the future an important role in Differential Geometry and Theoretical Physics, where they are known as s-models. These Proceedings develop both aspects of the theory, with a special attention to the constructive methods, in particular the so-called twistorial approach. It includes expository articles on the twistorial methods, the various appearence of σ-models in Physics, the powerful analytic theory of regularity of SCHOEN-UHLENBECK.

Author : Athanase Papadopoulos
Publisher : European Mathematical Society
Page : 812 pages
File Size : 51,7 Mb
Release : 2007
Category : Mathematics
ISBN : 3037190299

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Handbook of Teichmüller Theory by Athanase Papadopoulos Pdf

The Teichmuller space of a surface was introduced by O. Teichmuller in the 1930s. It is a basic tool in the study of Riemann's moduli spaces and the mapping class groups. These objects are fundamental in several fields of mathematics, including algebraic geometry, number theory, topology, geometry, and dynamics. The original setting of Teichmuller theory is complex analysis. The work of Thurston in the 1970s brought techniques of hyperbolic geometry to the study of Teichmuller space and its asymptotic geometry. Teichmuller spaces are also studied from the point of view of the representation theory of the fundamental group of the surface in a Lie group $G$, most notably $G=\mathrm{PSL}(2,\mathbb{R})$ and $G=\mathrm{PSL}(2,\mathbb{C})$. In the 1980s, there evolved an essentially combinatorial treatment of the Teichmuller and moduli spaces involving techniques and ideas from high-energy physics, namely from string theory. The current research interests include the quantization of Teichmuller space, the Weil-Petersson symplectic and Poisson geometry of this space as well as gauge-theoretic extensions of these structures. The quantization theories can lead to new invariants of hyperbolic 3-manifolds. The purpose of this handbook is to give a panorama of some of the most important aspects of Teichmuller theory. The handbook should be useful to specialists in the field, to graduate students, and more generally to mathematicians who want to learn about the subject. All the chapters are self-contained and have a pedagogical character. They are written by leading experts in the subject.

Author : Frédéric Hélein
Publisher : Cambridge University Press
Page : 298 pages
File Size : 48,5 Mb
Release : 2002-06-13
Category : Mathematics
ISBN : 0521811600

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Harmonic Maps, Conservation Laws and Moving Frames by Frédéric Hélein Pdf

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Author : Richard Schoen,Shing-Tung Yau
Publisher : Unknown
Page : 394 pages
File Size : 43,7 Mb
Release : 2013-04-30
Category : Electronic
ISBN : 1571462600

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

Author : Yuan-Jen Chiang
Publisher : Springer Science & Business Media
Page : 418 pages
File Size : 51,6 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.