1547671870-The_Ricci_Flow__Chow

Contents

Preface
A guide for the reader
A guide for the hurried reader
Acknowledgments

Chapter 1. The Ricci flow of special geometries

1. Geometrization of three-manifolds


2. Model geometries


3. Classifying three-dimensional maximal model geometries


4. Analyzing the Ricci flow of homogeneous geometries


5. The Ricci flow of a geometry with maximal isotropy SO (3)


6. The Ricci flow of a geometry with isotropy SO (2)


7. The Ricci flow of a geometry with trivial isotropy
   Notes and commentary

Chapter 2. Special and limit solutions

1. Generalized fixed points


2. Eternal solutions


3. Ancient solutions


4. Immortal solutions


5. The neckpinch


6. The degenerate neckpinch
   Notes and commentary

Chapter 3. Short time existence

1. Variation formulas


2. The linearization of the Ricci tensor and its principal symbol


3. The Ricci-DeTurck flow and its parabolicity


4. The Ricci-DeTurck flow in relation to the harmonic map flow


5. The Ricci flow regarded as a heat equation
   Notes and commentary

Chapter 4. Maximum principles

1. Weak maximum principles for scalar equations


2. Weak maximum principles for tensor equations


3. Advanced weak maximum principles for systems


4. Strong maximum principles
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