# Lecture: THE SHORT TIME ASYM...

2012-12-17 00:00 stxy View：[_showDynClicks("wbnews", 1370895784, 1409) ]

**THE SHORT TIME ASYMPTOTICS OF NASH ENTROPY**

Speaker:

**Dr.**GUOYI XU（UNIVERSITY OF CALIFORNIA, IRVINE）**Time: 10:00——11:00, 24, December**

**Place：Room 422**

**Abstract :**Let (M^n; g) be a complete Riemannian manifold, and H(x; y; t) is the heat kernel on M^n. In 1958, Nash introduced the so-called Nash entropy N(H; t) while proving the Holder continuity of solutions of parabolic equations. In 2002, Perelman introduced W-entropy for Ricci flow while solving Poincar´e conjecture. Amazingly, there are close relationships between those entropies. Motivated by one of Perelman’s claims in his celebrated preprints, we studied the asymptotic behavior of N(H; t) and \partial/(\partial t)[N(H; t)] as t→0^+, and got the asymptotic formulas at t = 0.

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