On Harmonic Maps Into Conic Surfaces
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On Harmonic Maps Into Conic Surfaces
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Author : Jesse David Gell-Redman
language : en
Publisher: Stanford University
Release Date : 2011
On Harmonic Maps Into Conic Surfaces written by Jesse David Gell-Redman and has been published by Stanford University this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011 with categories.
We prove the existence and uniqueness of harmonic maps in degree one homotopy classes of closed, orientable surfaces of positive genus, where the target has non-positive gauss curvature and conic points with cone angles less than $2\pi$. For a homeomorphism $w$ of such a surface, we prove existence and uniqueness of minimizers in the homotopy class of $w$ relative to the inverse images of the cone points with cone angles less than or equal to $\pi$. We show that such maps are homeomorphisms and that they depend smoothly on the target metric. For fixed geometric data, the space of minimizers in relative degree one homotopy classes is a complex manifold of (complex) dimension equal to the number of cone points with cone angles less than or equal to $\pi$. When the genus is zero, we prove the same relative minimization provided there are at least three cone points of cone angle less than or equal to $\pi$.
On Harmonic Maps Into Conic Surfaces
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Author : Jesse David Gell-Redman
language : en
Publisher:
Release Date : 2011
On Harmonic Maps Into Conic Surfaces written by Jesse David Gell-Redman and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011 with categories.
We prove the existence and uniqueness of harmonic maps in degree one homotopy classes of closed, orientable surfaces of positive genus, where the target has non-positive gauss curvature and conic points with cone angles less than $2\pi$. For a homeomorphism $w$ of such a surface, we prove existence and uniqueness of minimizers in the homotopy class of $w$ relative to the inverse images of the cone points with cone angles less than or equal to $\pi$. We show that such maps are homeomorphisms and that they depend smoothly on the target metric. For fixed geometric data, the space of minimizers in relative degree one homotopy classes is a complex manifold of (complex) dimension equal to the number of cone points with cone angles less than or equal to $\pi$. When the genus is zero, we prove the same relative minimization provided there are at least three cone points of cone angle less than or equal to $\pi$.
Harmonic Maps And Integrable Systems
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Author : John C. Wood
language : de
Publisher: Springer-Verlag
Release Date : 2013-07-02
Harmonic Maps And Integrable Systems written by John C. Wood and has been published by Springer-Verlag this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-07-02 with Mathematics categories.
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 Between Surfaces
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Author : Jürgen Jost
language : en
Publisher: Springer
Release Date : 2006-12-08
Harmonic Maps Between Surfaces written by Jürgen Jost and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-12-08 with Mathematics categories.
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.
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.
Constant Mean Curvature Surfaces Harmonic Maps And Integrable Systems
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Author : Frederic Hélein
language : en
Publisher: Birkhäuser
Release Date : 2012-12-06
Constant Mean Curvature Surfaces Harmonic Maps And Integrable Systems written by Frederic Hélein and has been published by Birkhäuser this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
This book intends to give an introduction to harmonic maps between a surface and a symmetric manifold and constant mean curvature surfaces as completely integrable systems. The presentation is accessible to undergraduate and graduate students in mathematics but will also be useful to researchers. It is among the first textbooks about integrable systems, their interplay with harmonic maps and the use of loop groups, and it presents the theory, for the first time, from the point of view of a differential geometer. The most important results are exposed with complete proofs (except for the last two chapters, which require a minimal knowledge from the reader). Some proofs have been completely rewritten with the objective, in particular, to clarify the relation between finite mean curvature tori, Wente tori and the loop group approach - an aspect largely neglected in the literature. The book helps the reader to access the ideas of the theory and to acquire a unified perspective of the subject.
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 Between Surfaces
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Author : Jurgen Jost
language : en
Publisher:
Release Date : 2014-01-15
Harmonic Maps Between Surfaces written by Jurgen Jost and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-01-15 with categories.