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Selected Topics in Harmonic Maps

About this Title

James Eells and Luc Lemaire

Publication: CBMS Regional Conference Series in Mathematics
Publication Year: 1983; Volume 50
ISBNs: 978-0-8218-0700-2 (print); 978-1-4704-2412-1 (online)
DOI: https://doi.org/10.1090/cbms/050
MathSciNet review: MR703510
MSC: Primary 58E20; Secondary 53C20

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Table of Contents

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Front/Back Matter

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Chapters

• Introduction
• Part I. Differential Geometric Aspects of Harmonic Maps
• 1. Operators on vector bundles
• 2. Harmonic maps
• 3. Some properties of harmonic maps
• 4. Second variation of the energy
• 5. Spheres and the behavior of the energy
• 6. The stress-energy tensor
• 7. Harmonic morphisms
• 8. Holomorphic and harmonic maps between almost Kähler manifolds
• 9. Properties of harmonic maps between Kähler manifolds
• Part II. Problems Relating to Harmonic Maps
• 1. Existence of harmonic maps
• 2. Regularity problems
• 3. Holomorphic and conformal maps
• 4. Construction/classification of harmonic maps
• 5. Properties of harmonic maps
• 6. Spaces of maps
• 7. Noncompact domains
• 8. Variations on a theme