Selected Topics in Harmonic Maps
Author : James Eells
Publisher : American Mathematical Soc.
Page : 108 pages
File Size : 23,98 MB
Release : 1983-01-01
Category : Mathematics
ISBN : 9780821888957
Selected Topics in Harmonic Maps
Author : James Eells
Publisher : American Mathematical Soc.
Page : 93 pages
File Size : 42,10 MB
Release : 1983
Category : Mathematics
ISBN : 0821807005
Book Description
Gives an account of the various aspects of the theory of harmonic maps between Riemannian manifolds. This book presents an exposition of the qualitative aspects of harmonic maps. It also proposes certain unsolved problems, together with comments and references, which are of widely varying difficulty.
Harmonic Maps Between Surfaces
Author : Jürgen Jost
Publisher : Springer
Page : 143 pages
File Size : 25,5 MB
Release : 2006-12-08
Category : Mathematics
ISBN : 3540388680
Book Description
Two Reports On Harmonic Maps
Author : James Eells
Publisher : World Scientific
Page : 229 pages
File Size : 23,32 MB
Release : 1995-03-29
Category : Mathematics
ISBN : 9814502928
Book Description
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.
Harmonic Mappings, Twistors And Sigma Models
Author : Paul Gauduchon
Publisher : World Scientific
Page : 390 pages
File Size : 21,95 MB
Release : 1988-10-01
Category : Mathematics
ISBN : 9813201487
Book Description
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.
Calculus of Variations and Harmonic Maps
Author : Hajime Urakawa
Publisher : American Mathematical Soc.
Page : 272 pages
File Size : 42,68 MB
Release : 2013-02-15
Category : Mathematics
ISBN : 0821894137
Book Description
This book provides a wide view of the calculus of variations as it plays an essential role in various areas of mathematics and science. Containing many examples, open problems, and exercises with complete solutions, the book would be suitable as a text for graduate courses in differential geometry, partial differential equations, and variational methods. The first part of the book is devoted to explaining the notion of (infinite-dimensional) manifolds and contains many examples. An introduction to Morse theory of Banach manifolds is provided, along with a proof of the existence of minimizing functions under the Palais-Smale condition. The second part, which may be read independently of the first, presents the theory of harmonic maps, with a careful calculation of the first and second variations of the energy. Several applications of the second variation and classification theories of harmonic maps are given.
Harmonic Mappings and Minimal Immersion
Author : Enrico Giusti
Publisher : Springer
Page : 295 pages
File Size : 24,95 MB
Release : 2006-11-14
Category : Mathematics
ISBN : 3540397167
Book Description
Developments of Harmonic Maps, Wave Maps and Yang-Mills Fields into Biharmonic Maps, Biwave Maps and Bi-Yang-Mills Fields
Author : Yuan-Jen Chiang
Publisher : Springer Science & Business Media
Page : 418 pages
File Size : 18,75 MB
Release : 2013-06-18
Category : Mathematics
ISBN : 3034805349
Book Description
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.
Harmonic Maps and Differential Geometry
Author : Eric Loubeau
Publisher : American Mathematical Soc.
Page : 296 pages
File Size : 28,15 MB
Release : 2011
Category : Mathematics
ISBN : 0821849875
Book Description
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.
Harmonic Maps
Author : U. R. J. Knill
Publisher : Springer
Page : 167 pages
File Size : 47,14 MB
Release : 2006-11-15
Category : Mathematics
ISBN : 3540393609
