Title: Hamilton’s gradient estimates
 

Speaker: 朱晓宝(中国人民大学)

Venue: Room 09 at Quan-Zhai (全斋), New location for BICMR, Peking University

Time: May 9, 2012, Wednesday, 10:10-12:00am

Abstract: In this talk, I will first introduce Hamilton’s gradient estimates for heat equations on Riemannian manifolds (both the compact and noncompact cases). Then I will give application of them to estimate the heat kernel. Finally, I prepare to give some generalizations of Hamilton’s gradient estimate to nonlinear parabolic equations (e.g. the fast diffusion equation, the heat equation with a nonlinear term and so on).

The results above takes form the following papers:

1. R. S. Hamilton, A matrix Harnack estimate for the heat equation, Comm. Anal. Geom. 1 (1993), 113-126.

2. P. Souplet and Qi S. Zhang, Sharp gradient estimate and Yau’s Liouville theorem for the heat equation on noncompact manifolds, Bull. London Math. Soc. 38 (2006), 1045-1053.

3. B. L. Kotschwar, Hamilton’s gradient estimate for the heat kernel on complete manifolds, Proc. Amer. Math. Soc. 135 (2007), no. 9, 3013-3019.

4. X. B. Zhu, Hamilton's gradient estimates and Liouville theorems for fast diffusion equations on noncompact Riemannian manifolds, Proc. Amer. Math. Soc. 139 (2011), 1637-1644.