vi CONTENTS
The equivalence of Q and Q
Notes and commentary
Chapter 30. Type I Singularities and Ancient Solutions
l. Reduced distance of Type A solutions
- Reduced volume at the singular time for Type I solutions
- Type I solutions have shrinker singularity models
- Some results on Type I ancient solutions
- Notes and commentary
Chapter 31. Hyperbolic Geometry and 3-Manifolds
l. Introduction to hyperbolic space
- Topology and geometry of hyperbolic 3-manifolds
- The Margulis lemma and hyperbolic cusps
- Mostow rigidity
- Seifert fibered manifolds and graph manifolds
- Notes and commentary
Chapter 32. Nonsingular Solutions on Closed 3-Manifolds
l. Introduction
- The main result on nonsingular solutions
- The three cases of nonsingular solutions
- The positive and zero cases of nonsingular solutions
- The negative case-sequential limits must b e hyperbolic
- Notes and commentary
Chapter 33. Noncompact Hyperbolic Limits
l. Main results on hyperbolic pieces
- Harmonic maps parametrizing almost hyperbolic pieces
- Proof of the stability of hyperbolic limits
- Incompressibility of boundary tori of hyperbolic pieces
- Notes and commentary
Chapter 34. Constant Mean Curvature Surfaces and Harmonic Maps
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169
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185
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211213
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226
237
254by IFT 257l. Constant mean curvature surfaces 257
- Harmonic maps near the identity of sn 260
- Existence of harmonic maps near the identity of manifolds with
negative Ricci curvature 266 - Application of Mostow rigidity to the existence of isometries 273
- Notes and commentary 278
Chapter 35. Stability of Ricci Flow
l. Linear stability of Ricci flow
- Analytic semigroups and maximal regularity theory
- Dynamic stability results obtained using linearization
- Dynamic stability results obtained by other methods