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285G, Lecture 3: The maximum principle, and the pinching phenomenon

We now begin the study of (smooth) solutions to the Ricci flow equation

, (1)

particularly for compact manifolds in three dimensions. Our first basic tool will be the… 4,406 more words


285G, Lecture 0: Riemannian manifolds and curvature

Next week (starting on Wednesday, to be more precise), I will begin my class on Perelman’s proof of the PoincarĂ© conjecture. As I only have ten weeks in which to give this proof, I will have to move rapidly through some of the more basic aspects of… 4,830 more words