Comparison geometry of Bakry-Emery Ricci curvature on Riemannian manifolds with weighted measure (I)(II)
李向東教授中國科學院數學與系統科學研究院 上午 10:00–12:00 鴻經館 107 室Abstract:
In recent years, the Bakry-Emery Ricci curvature has been received a lot of attentions in stochastic analysis and geometric analysis. In this series of lectures, I will present some recent results in the study of various problems in geometric analysis and stochastic analysis on Riemannian manifolds with weighted measure. After an introduction of the Bakry-Emery Ricci curvature and related materials, I will present the following topics in my lectures:
Lecture 1. Liouville theorems and Cheeger-Gromoll splitting theorem on manifolds with weighted measure
Lecture 2. Harnack inequalities, eigenvalue and heat kernel estimates
of Witten Laplacian on manifolds