题目： Li-Yau gradient bounds without Ricci curvature lower bound
报告人: 朱萌教授 (华东师范大学)
时间: 12月19日（周四）下午 2:00--3:00.
摘要: Li-Yau type gradient bounds have been widely used in geometric analysis, and become a powerful tool in exploring geometric and topological properties of differential manifolds. Since the celebrated work of P. Li and S.-T. Yau, numerous efforts have been made in improving the Li-Yau bound on manifolds with Ricci curvature bounded from below. In this talk, we will present our recent works on Li-Yau type gradient bounds for positive solutions of the heat equation on complete manifolds with certain integral curvature bounds, namely, |Ric_| in L^p for p>n/2 or Kato type norm of |Ric_| being bounded together with a Gaussian upper bound of the heat kernel. These assumptions allow the lower bound of the Ricci curvature to tend to negative infinity, which is weaker than the assumptions in the known results. We will also introduce a Li-Yau type bound for the heat equation under the compact Ricci flow with uniformly bounded scalar curvature. These are joint works with Qi S. Zhang.