5 edition of **Harmonic Maps** found in the catalog.

- 294 Want to read
- 20 Currently reading

Published
**November 1992**
by World Scientific Pub Co Inc
.

Written in English

- Analytic topology,
- Differential & Riemannian geometry,
- Differential Geometry,
- Science/Mathematics,
- Mathematics,
- Harmonic maps

The Physical Object | |
---|---|

Format | Hardcover |

Number of Pages | 452 |

ID Numbers | |

Open Library | OL9193849M |

ISBN 10 | 9810207042 |

ISBN 10 | 9789810207045 |

Y is a harmonic map relative to Riemannian metrics g and h, and if e(X)+Id~e(Y)l >0, then ~p is holomorphic relative to the complex structures determined by g and h. Here e (X) = 2 - 2p and e (Y) = 2 - 2q denote Euler characteristics; and d, is the degree of cp. cp is holomorphic means that cp is either holomorphic or by: This book is concerned with harmonic maps into homogeneous spaces and focuses upon maps of Riemann surfaces into flag manifolds, to bring results of 'twistor methods' for symmetric spaces into a unified framework by using the theory of compact .

The harmonic map energy Deﬁnition of energy and area Given a suﬃciently smooth map u: M! N between smooth closed Riemannian manifolds (M,g) and N =(N,G) of any dimension, we can deﬁne the harmonic map energy E(u)=E(u,g):= 1 2 Z M |du|2 gdµ g. Smooth critical points are known as harmonic maps. By this, we mean that u is a harmonic mapFile Size: KB. Zygmund's two volume books on trigonometric series are good, but I would tackle a few other books on harmonic analysis before going for it. It is quite complex in comparison to the other references and will not help much if you do not already have a foundation in harmonic.

4. Quasi-Harmonic Maps In order to motivate the ensuing discussion, we start with the following simple problem: Given a single triangle of a surface mesh and a map gthat carries the triangle into a cor-responding triangle in the planar domain. Solely from the properties of the map g, we can establish a second map fFile Size: 3MB. HARMONIC MAPPINGS OF RIEMANNIAN MANIFOLDS. 11 Chapter II. Deformations of maps. 6. Deformations by the heat equation 7. Global equations 8. Derivative bounds for the elliptic case 9. Bounds for the parabolic case Successive approximations Harmonic mappings Added in proof: The theory of the energy functional (and its harmonic.

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It introduces the necessary mathematical tools for the study of harmonic maps and presents applications of the methods and theory, bringing in results from recent research on the regularity of weak solutions.

The book will be of particular interest to graduate students and researchers in geometry, analysis and partial differential by: 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 Cited by: 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. Harmonic maps are generalisations of the concept of geodesics.

They encompass many fundamental examples in differential geometry and have recently become of widespread use in many areas of mathematics and mathematical : Martin A. Guest. Harmonic maps between smooth Riemannian manifolds play a ubiquitous role in differential geometry.

Examples include geodesics viewed as maps, minimal surfaces, holomorphic maps and Abelian. Harmonic Maps Proceedings of the N.S.F.-C.B.M.S. Regional Conference, Held at Tulane University, New Orleans, DecemberHarmonic curvature for gravitational and Yang-Mills fields. Pages Bourguignon, Jean-Pierre.

Harmonic Maps Book Subtitle Proceedings of the N.S.F.-C.B.M.S. Regional Conference, Held at Tulane. The book begins by introducing these concepts, stressing the interplay between geometry, the role of symmetries and weak solutions.

It then presents a guided tour into the theory of completely integrable systems for harmonic maps, followed by two chapters devoted to recent results on the regularity of weak solutions.

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. harmonic maps. On the way, we mention harmonic morphisms: maps between Riemannian manifolds which pre-serve Laplace’s equation; these turn out to be a particular class of harmonic maps and exhibit some properties dual to those of harmonic maps.

More information on harmonic maps can be found in the following articles and books; for File Size: KB. Harmonic maps are the 'least expanding' maps in orthogonal directions. Existence of harmonic maps from a complete Riemannian manifold to a complete Riemannian manifold of non-positive sectional curvature was proved by Eells & Sampson ().

A harmonic map f: M → E m of a Riemann surface M is called a branched (or generalized) minimal immersion if it is conformal except at the branch points, and the image f(M) is called a branched minimal surface. Book Description. This book is concerned with harmonic maps into homogeneous spaces and focuses upon maps of Riemann surfaces into flag manifolds, to bring results of 'twistor methods' for symmetric spaces into a unified framework by using the theory of compact Lie groups and complex differential geometry.

The book can be used as a textbook for the topic course of advanced graduate students and for researchers who are interested in geometric partial differential equations and geometric analysis.

Sample Chapter(s) Chapter 1: Introduction to harmonic maps ( KB) Contents: Introduction to Harmonic Maps; Regularity of Minimizing Harmonic Maps. To become acquainted to some of these, the reader is referred to two reports and a survey paper by Eells and Lemaire [,] about the developments of harmonic maps up to for details.

Several books on harmonic maps [. Lectures on harmonic maps Volume 2 of Conference proceedings and lecture notes in geometry and topology Monographs in Geometry & Topology No 3: Authors: Richard M.

Schoen, Shing-Tung Yau: Publisher: International Press, Original from: the University of Michigan: Digitized: Feb 5, Length: pages: Subjects.

Wave maps are harmonic maps on Minkowski spaces and have been studied since the s. Yang-Mills fields, the critical points of Yang-Mills functionals of connections whose curvature tensors are harmonic, were explored by a few physicists in the s, and biharmonic maps (generalizing harmonic maps) were introduced by Guoying Jiang in 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. Harmonic maps 13 3. Some properties of harmonic maps 21 4.

Second Variation of the energy 27 5. Spheres and the behavior of the energy 32 6. The stress-energy tensor 38 7. Harmonic morphisms 41 8. Holomorphic and harmonic maps between almost Kahler manifolds 47 9. Properties of harmonic maps between Kahler manifolds 53 Part II.

This book attempts to present a comprehensive survey on biharmonic submanifolds and biharmonic maps from the view points of Riemannian geometry. This book is. 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, σ-models in physics. This book presents these two reports in a single volume with a brief supplement reporting on some.

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.

Harmonic maps and the related theory of minimal surfaces are variational problems of long standing in differential geometry. Many important advances have been Harmonic Maps Into Homogeneous Spaces book. By Malcolm Black.

Edition 1st Edition. First Published eBook Published 4 May Pub. location New by: This book provides a broad yet comprehensive introduction to the analysis of harmonic maps and their heat flows. The first part of the book contains many important theorems on the regularity of minimizing harmonic maps by Schoen-Uhlenbeck, stationary harmonic maps between Riemannian manifolds in higher dimensions by Evans and Bethuel, and weakly harmonic maps .