Harmonic Maps And Differential Geometry
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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 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 Mathematics 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.
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.
The Analysis Of Harmonic Maps And Their Heat Flows
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Author : Fanghua Lin
language : en
Publisher: World Scientific
Release Date : 2008
The Analysis Of Harmonic Maps And Their Heat Flows written by Fanghua Lin and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008 with Science categories.
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.
Seminar On Nonlinear Partial Differential Equations
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Author : S.S. Chern
language : en
Publisher: Springer
Release Date : 1984-11-01
Seminar On Nonlinear Partial Differential Equations written by S.S. Chern and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 1984-11-01 with Mathematics categories.
When the Mathematical Sciences Research Institute was started in the Fall of 1982, one of the programs was "non-linear partial differential equations". A seminar was organized whose audience consisted of graduate students of the University and mature mathematicians who are not experts in the field. This volume contains 18 of these lectures. An effort is made to have an adequate Bibliography for further information. The Editor wishes to take this opportunity to thank all the speakers and the authors of the articles presented in this volume for their cooperation. S. S. Chern, Editor Table of Contents Geometrical and Analytical Questions Stuart S. Antman 1 in Nonlinear Elasticity An Introduction to Euler's Equations Alexandre J. Chorin 31 for an Incompressible Fluid Linearizing Flows and a Cohomology Phillip Griffiths 37 Interpretation of Lax Equations The Ricci Curvature Equation Richard Hamilton 47 A Walk Through Partial Differential Fritz John 73 Equations Remarks on Zero Viscosity Limit for Tosio Kato 85 Nonstationary Navier-Stokes Flows with Boundary Free Boundary Problems in Mechanics Joseph B. Keller 99 The Method of Partial Regularity as Robert V.
Differential Geometry Partial Differential Equations On Manifolds
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Author : Robert Everist Greene
language : en
Publisher: American Mathematical Soc.
Release Date : 1993
Differential Geometry Partial Differential Equations On Manifolds written by Robert Everist Greene 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 1993 with Mathematics categories.
The first of three parts comprising Volume 54, the proceedings of the Summer Research Institute on Differential Geometry, held at the University of California, Los Angeles, July 1990 (ISBN for the set is 0-8218-1493-1). Part 1 begins with a problem list by S.T. Yau, successor to his 1980 list ( Sem
Differential Geometry And Analysis On Cr Manifolds
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Author : Sorin Dragomir
language : en
Publisher: Springer Science & Business Media
Release Date : 2007-06-10
Differential Geometry And Analysis On Cr Manifolds written by Sorin Dragomir 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 2007-06-10 with Mathematics categories.
Presents many major differential geometric acheivements in the theory of CR manifolds for the first time in book form Explains how certain results from analysis are employed in CR geometry Many examples and explicitly worked-out proofs of main geometric results in the first section of the book making it suitable as a graduate main course or seminar textbook Provides unproved statements and comments inspiring further study