Souplet-Zhang type estimate and Li-Yau inequality under integral Ricci curvature condition

Speaker: meng zhu(East China Normal University)
Time: Friday 23 May, 9:30-11:30
Location: R1610, SIMIS
Zoom Meeting ID: 479 937 5280(Passcode: SIMIS)

Abstract：
On a closed n-dimensional Riemannian manifold, assuming that the L^1 Kato integral of the Ricci curvature tensor is bounded, we prove a Souplet-Zhang type gradient estimate for bounded positive solutions of the heat equation. Then, by implanting the Souplet-Zhang type estimate in an argument of Qi S. Zhang, we show that certain integral Li-Yau inequality holds for the heat equation under this circumstance. The curvature assumption includes the Ricci curvature tensor being L^p (p>n) integrable and volume bing noncollapsed. This is a joint work with Xingyu Song, Ling Wu, and Qi S. Zhang.