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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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.

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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Partial Regularity for Harmonic Maps and Related Problems

Partial Regularity for Harmonic Maps and Related Problems
Title Partial Regularity for Harmonic Maps and Related Problems PDF eBook
Author Roger Moser
Publisher World Scientific
Pages 196
Release 2005
Genre Mathematics
ISBN 9812560858

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The book presents a collection of results pertaining to the partial regularity of solutions to various variational problems, all of which are connected to the Dirichlet energy of maps between Riemannian manifolds, and thus related to the harmonic map problem. The topics covered include harmonic maps and generalized harmonic maps; certain perturbed versions of the harmonic map equation; the harmonic map heat flow; and the Landau-Lifshitz (or Landau-Lifshitz-Gilbert) equation. Since the methods in regularity theory of harmonic maps are quite subtle, it is not immediately clear how they can be applied to certain problems that arise in applications. The book discusses in particular this question.

The Analysis of Harmonic Maps and Their Heat Flows

The Analysis of Harmonic Maps and Their Heat Flows
Title The Analysis of Harmonic Maps and Their Heat Flows PDF eBook
Author Fanghua Lin
Publisher World Scientific
Pages 280
Release 2008
Genre Science
ISBN 9812779523

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This book contains the proceedings of the Fourth Meeting on CPT and Lorentz Symmetry, held at Indiana University in Bloomington on August 8-11, 2007. The Meeting focused on experimental tests of these fundamental symmetries and on important theoretical issues, including scenarios for possible relativity violations. Experimental subjects covered include: astrophysical observations, clock-comparison measurements, cosmological birefringence, electromagnetic resonant cavities, gravitational tests, matter interferometry, muon behavior, neutrino oscillations, oscillations and decays of neutral mesons, particle-antiparticle comparisons, post-Newtonian gravity, space-based missions, spectroscopy of hydrogen and antihydrogen, and spin-polarized matter.Theoretical topics covered include: physical effects at the level of the Standard Model, General Relativity, and beyond; the possible origins and mechanisms for Lorentz and CPT violations; and associated issues in field theory, particle physics, gravity, and string theory. The contributors consist of the leading experts in this very active research field.

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.