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Intro
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Classroom Contents
Harmonic Maps and Rigidity
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- 1 Intro
- 2 Harmonic maps between Riemannian manifolds
- 3 Harmonic maps into CAT(0) spaces
- 4 Existence theory of harmonic maps
- 5 Mostow and Margulis Rigidity
- 6 Mostow's strong rigidity - geometric version
- 7 Harmonic maps approach to Rigidity
- 8 Siu's Holomorphic Rigidity
- 9 Mok-Siu-Yeung's Geometric Rigidity
- 10 Uniform lattice vs. Non-uniform lattice
- 11 Non-compact domains
- 12 Idea of the proof
- 13 The Bochner method
- 14 Existence of harmonic map for the compact case
- 15 Infinite energy harmonic maps in dime=1
- 16 Proof of existence of infinite energy maps
- 17 Proof in dimensions 2
- 18 Sketch of the existence of harmonic map
- 19 Sketch of the proof of pluriharmonicity
- 20 Proof in higher dimensions
- 21 Teichmüller theory
- 22 Integral rigidity
- 23 Fundamental group of a quasi-projective variety
