Selected Topics in Harmonic Maps

Selected Topics in Harmonic Maps
Title Selected Topics in Harmonic Maps PDF eBook
Author James Eells
Publisher American Mathematical Soc.
Pages 93
Release 1983
Genre Mathematics
ISBN 0821807005

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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.

Selected Topics in Harmonic Maps

Selected Topics in Harmonic Maps
Title Selected Topics in Harmonic Maps PDF eBook
Author James Eells
Publisher American Mathematical Soc.
Pages 108
Release 1983-01-01
Genre Mathematics
ISBN 9780821888957

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Selected Topics in Harmonic Maps

Selected Topics in Harmonic Maps
Title Selected Topics in Harmonic Maps PDF eBook
Author
Publisher
Pages
Release 1983
Genre
ISBN

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Geometry of Harmonic Maps

Geometry of Harmonic Maps
Title Geometry of Harmonic Maps PDF eBook
Author Yuanlong Xin
Publisher Springer Science & Business Media
Pages 264
Release 1996-04-30
Genre Mathematics
ISBN 9780817638207

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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.

Harmonic Mappings, Twistors And Sigma Models

Harmonic Mappings, Twistors And Sigma Models
Title Harmonic Mappings, Twistors And Sigma Models PDF eBook
Author Paul Gauduchon
Publisher World Scientific
Pages 390
Release 1988-10-01
Genre Mathematics
ISBN 9813201487

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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.

Harmonic Mappings and Minimal Immersion

Harmonic Mappings and Minimal Immersion
Title Harmonic Mappings and Minimal Immersion PDF eBook
Author Enrico Giusti
Publisher Springer
Pages 295
Release 2006-11-14
Genre Mathematics
ISBN 3540397167

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Developments of Harmonic Maps, Wave Maps and Yang-Mills Fields into Biharmonic Maps, Biwave Maps and Bi-Yang-Mills Fields

Developments of Harmonic Maps, Wave Maps and Yang-Mills Fields into Biharmonic Maps, Biwave Maps and Bi-Yang-Mills Fields
Title Developments of Harmonic Maps, Wave Maps and Yang-Mills Fields into Biharmonic Maps, Biwave Maps and Bi-Yang-Mills Fields PDF eBook
Author Yuan-Jen Chiang
Publisher Springer Science & Business Media
Pages 418
Release 2013-06-18
Genre Mathematics
ISBN 3034805349

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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.