Harmonic Maps And Differential Geometry
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Harmonic Maps And Differential Geometry
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Author : Eric Loubeau
language : en
Publisher: American Mathematical Soc.
Release Date : 2011
Harmonic Maps And Differential Geometry written by Eric Loubeau and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011 with Geometry, Differential categories.
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.
Two Reports On Harmonic Maps
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Author : James Eells
language : en
Publisher: World Scientific
Release Date : 1995
Two Reports On Harmonic Maps written by James Eells and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 1995 with Mathematics categories.
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 Khlerian 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.
Geometry Of Harmonic Maps
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Author : Yuanlong Xin
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Geometry Of Harmonic Maps written by Yuanlong Xin and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
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 Maps And Minimal Immersions With Symmetries
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Author : James Eells
language : en
Publisher: Princeton University Press
Release Date : 1993
Harmonic Maps And Minimal Immersions With Symmetries written by James Eells and has been published by Princeton University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1993 with Mathematics categories.
The aim of this book is to study harmonic maps, minimal and parallel mean curvature immersions in the presence of symmetry. In several instances, the latter permits reduction of the original elliptic variational problem to the qualitative study of certain ordinary differential equations: the authors' primary objective is to provide representative examples to illustrate these reduction methods and their associated analysis with geometric and topological applications. The material covered by the book displays a solid interplay involving geometry, analysis and topology: in particular, it includes a basic presentation of 1-cohomogeneous equivariant differential geometry and of the theory of harmonic maps between spheres.
Calculus Of Variations And Harmonic Maps
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Author : Hajime Urakawa
language : en
Publisher: American Mathematical Soc.
Release Date : 2013-02-15
Calculus Of Variations And Harmonic Maps written by Hajime Urakawa and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-02-15 with categories.
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 Maps Into Homogeneous Spaces
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Author : Malcolm Black
language : en
Publisher: Routledge
Release Date : 2018-05-04
Harmonic Maps Into Homogeneous Spaces written by Malcolm Black and has been published by Routledge this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-05-04 with Mathematics categories.
Harmonic maps and the related theory of minimal surfaces are variational problems of long standing in differential geometry. Many important advances have been made in understanding harmonic maps of Riemann surfaces into symmetric spaces. In particular, ""twistor methods"" construct some, and in certain cases all, such mappings from holomorphic data. These notes develop techniques applicable to more general homogeneous manifolds, in particular a very general twistor result is proved. When applied to flag manifolds, this wider viewpoint allows many of the previously unrelated twistor results for symmetric spaces to be brought into a unified framework. These methods also enable a classification of harmonic maps into full flag manifolds to be established, and new examples are constructed. The techniques used are mostly a blend of the theory of compact Lie groups and complex differential geometry. This book should be of interest to mathematicians with experience in differential geometry and to theoretical physicists.
Harmonic Maps And Minimal Immersions With Symmetries Am 130 Volume 130
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Author : James Eells
language : en
Publisher: Princeton University Press
Release Date : 2016-03-02
Harmonic Maps And Minimal Immersions With Symmetries Am 130 Volume 130 written by James Eells and has been published by Princeton University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-03-02 with Mathematics categories.
The aim of this book is to study harmonic maps, minimal and parallel mean curvature immersions in the presence of symmetry. In several instances, the latter permits reduction of the original elliptic variational problem to the qualitative study of certain ordinary differential equations: the authors' primary objective is to provide representative examples to illustrate these reduction methods and their associated analysis with geometric and topological applications. The material covered by the book displays a solid interplay involving geometry, analysis and topology: in particular, it includes a basic presentation of 1-cohomogeneous equivariant differential geometry and of the theory of harmonic maps between spheres.
Harmonic Maps Between Riemannian Polyhedra
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Author : James Eells
language : en
Publisher: Cambridge University Press
Release Date : 2001-07-30
Harmonic Maps Between Riemannian Polyhedra written by James Eells and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2001-07-30 with Mathematics categories.
A research level book on harmonic maps between singular spaces, by renowned authors, first published in 2001.
Lectures On Harmonic Maps
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Author : Richard M. Schoen
language : en
Publisher: International Press of Boston
Release Date : 1997
Lectures On Harmonic Maps written by Richard M. Schoen and has been published by International Press of Boston this book supported file pdf, txt, epub, kindle and other format this book has been release on 1997 with Mathematics categories.
A presentation of research on harmonic maps, based on lectures given at the University of California, San Diego. Schoen has worked to use the Fells/Sampson theorem to reprove the rigidity theorem of Masfow and superrigidity theorem of Marqulis. Many of these developments are recorded here.
Harmonic Maps Loop Groups And Integrable Systems
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Author : Martin A. Guest
language : en
Publisher: Cambridge University Press
Release Date : 1997-01-13
Harmonic Maps Loop Groups And Integrable Systems written by Martin A. Guest and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1997-01-13 with Mathematics categories.
University-level introduction that leads to topics of current research in the theory of harmonic maps.