Two Reports on Harmonic Maps

By: James Eelles, Luc Lumaire

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Hardcover | 1 December 1994

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228 Pages

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Harmonic maps between Riemannian manifolds are solutions of systems of partial differential equations which appear in different contexts of differential geometry. They include holomorphic maps, minimal surfaces, delta-models in physics. Recently, they have become powerful tools in the study of global properties of Riemannian and Kahlerian manifolds. Standard references for this subject are two 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 source of reference, providing an organized exposition of results spread throughout more than 800 papers.

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Non-Fiction Mathematics Calculus & Mathematical Analysis Differential Calculus & Equations Geometry Differential & Riemannian Geometry Topology Analytic Topology Analytic Geometry Science Physics Booktopia Publisher Services

World Scientific Publishing

Foreword
Operations on vector bundles	p. 4
Harmonic maps	p. 8
Composition properties	p. 14
Maps into manifolds of nonpositive [actual symbol not reproducible] curvature	p. 18
The existence theorem for Riem [actual symbol not reproducible]	p. 22
Maps into flat manifolds	p. 29
Harmonic maps between spheres	p. 32
Holomorphic maps	p. 38
Harmonic maps of a surface	p. 42
Harmonic maps between surfaces	p. 48
Harmonic maps of manifolds with boundary	p. 55
Harmonic maps	p. 71
Regularity theory	p. 79
Maps of Kahler manifolds	p. 89
Maps of surfaces	p. 100
Second variation	p. 111
Twistor constructions	p. 120
Maps into groups and Grassmannians	p. 131
Maps into loop spaces	p. 141
Maps into spheres	p. 148
Non-compact manifolds	p. 158
Manifolds with boundary	p. 171
References	p. 186
Not Another Report on Harmonic Maps	p. 209
Index	p. 211
Table of Contents provided by Blackwell. All Rights Reserved.

Two Reports on Harmonic Maps

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