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Harmonic Maps, Conservation Laws and Moving Framesby Frédéric Hélein; B. Bollobas; W. Fulton; A. Katok; F. Kirwan; P. Sarnak
Cambridge University Press 2002; US$ 112.00An accessible and self-contained introduction to harmonic map theory and its analytical aspects, covering recent developments in the regularity theory of weakly harmonic maps. The book will be of particular interest to graduate students and researchers in geometry, analysis of partial differential equations and mathematical physics. more...
Harmonic Mappings in the Planeby Peter Duren; B. Bollobas; W. Fulton; A. Katok; F. Kirwan; P. Sarnak; B. Simon
Cambridge University Press 2004; US$ 77.00This first comprehensive account of the theory of planar harmonic mappings, meant for non-specialists, treats both the generalizations of univalent analytic functions and the connections with minimal surfaces. Included are background material in complex analysis and a full development of the classical theory of minimal surfaces, including the Weierstrass-Enneper representation. more...
Partial Regularity For Harmonic Maps And Related Problemsby Roger Moser
World Scientific 2005; US$ 103.00The 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. more...
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