报告人：朱萌

主持人：邱瑞锋 教授

时  间：10月16日13:00-13:45

地  点：闵行校区数学楼102报告厅

报告内容简介：

  In 1986, P. Li and S.T. Yau discovered the celebrated Li-Yau gradient estimate for the heat equation on Riemannian manifolds with Ricci curvature bounded from below. Since then Li-Yau type estimates have been widely used in geometric analysis, and become a powerful tool in deriving geometric and topological properties of differentiable manifolds. Meanwhile, numerous efforts have been made on improving or generalizing the Li-Yau estimate. However, it is to our knowledge that all known results rely on certain pointwise lower bound of the Ricci curvature.

  In this talk, we will present some Li-Yau type gradient estimates depending on certain integral bounds of the Ricci curvature. These assumptions may remain satisfied for a sequence of manifolds on which the lower bound of the Ricci curvature tends to negative infinity. Also, some elementary applications will be discussed. These are joint works with Qi S. Zhang.