-non-collapsed ancient solutionsRicci flow and Poincare conjecture by John Morgan 、Gang Tian(田剛 1958~)
Part I Introduction
Chapter 1. Preliminaries from Riemannian geometry
Riemannian metrics |
Curvature (Curvature2)Bianchi identity Uniformization Theorem |
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Hopf-Rinow theorem |
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Gaussian normal coordinates |
comparison theorem |
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Chapter 2. Manifold of non-negative curvature
Chapter 3. Basics of Ricci flow 何謂孤立子(Soliton)
Chapter 4. The maximum principle
Chapter 5. Covergence results for Ricci flow
Part II Perelman's length function and its applications
Chapter 6. A comparison geometry approach to the Ricci flow
Chapter 7. Complete Ricci flows of bounded curvature
Chapter 8. Non-collapsed results
Chapter 9. -non-collapsed ancient solutions
Chapter 10. Bounded curvature at bounded distance
Chapter 11. Geometric limits of generalized Ricci flow
Chapter 12. The standard soluton
Part III Ricci flow with surgery
Chapter 13. Surgery on a 
Chapter 14. Ricci flow with surgery : the difinition
Chapter 15. Controlled Ricci flow with surgery
Chapter 16. Proof of the non-collapsing
Chapter 17. Completion of the proof of Theorem 15.9
Part IV Completion of the proof of the Poincare Conjecture
Chapter 18. Finite-time extinction
Chapter 19. Completion of the proof Proposition 18.24