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285G, Lecture 10: Variation of L-geodesics, and monotonicity of Perelman reduced volume

Having completed a heuristic derivation of the monotonicity of Perelman reduced volume (Conjecture 1 from the previous lecture), we now turn to a rigorous proof. 3,157 more words


285G, Lecture 9: Comparison geometry, the high-dimensional limit, and Perelman reduced volume

We now turn to Perelman’s second scale-invariant monotone quantity for Ricci flow, now known as the Perelman reduced volume. We saw in the previous lecture that the monotonicity for Perelman entropy was ultimately derived (after some twists and turns) from the monotonicity of a potential under gradient flow. 3,708 more words