THE SHORT TIME ASYMPTOTICS OF NASH ENTROPY
Speaker: Dr. GUOYI XU（UNIVERSITY OF CALIFORNIA, IRVINE）
Time: 10:00——11:00, 24, December
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.