Notes on Harmonic Maps
Georgios Daskalopoulos, Chikako Mese

TL;DR
This paper provides an overview of harmonic maps between Riemannian manifolds, discussing existence, regularity, pluriharmonic maps, and key theorems relevant to non-Abelian Hodge theory.
Contribution
It compiles and explains fundamental concepts and recent results in harmonic maps, serving as educational notes for a summer school on non-Abelian Hodge theory.
Findings
Discussion of existence and regularity results
Introduction to pluriharmonic maps and Siu-Sampson formula
Explanation of Donaldson-Corlette theorem
Abstract
This is set of notes prepared for the Summer School on non-Abelian Hodge theory in Abbaye de Saint-Jacut de la Mer June, 6-19, 2022. We cover the following topics: Lecture 1. Harmonic Maps Between Riemannian Manifolds Lecture 2. Existence and Regularity Lecture 3. Pluriharmonic Maps and the Siu-Sampson Formula Lecture 4. Donaldson Corlette Theorem
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Taxonomy
TopicsAlgebraic Geometry and Number Theory · Geometric Analysis and Curvature Flows · Geometry and complex manifolds
