Lectures on the Ricci Flow (Paperback)

1. Introduction; 2. Riemannian geometry background; 3. The maximum principle; 4. Comments on existence theory for parabolic PDE; 5. Existence theory for the Ricci flow; 6. Ricci flow as a gradient flow; 7. Compactness of Riemannian manifolds and flows; 8. Perelman's W entropy functional; 9. Curvature pinching and preserved curvature properties under Ricci flow; 10. Three-manifolds with positive Ricci curvature and beyond.