EVENT DETAILS AND ABSTRACT

Title: Gradient Estimates for the Heat Equation on Manifolds with Boundary
Speaker: Artem Pulemotov
Speaker Info: University of Chicago
Brief Description:
Special Note:
Abstract:

The first part of the talk will discuss gradient estimates for the heat equation on a manifold~$M$ with nonempty boundary and a fixed Riemannian metric. We will mainly focus on Li-Yau-type inequalities. The second part of the talk will deal with the heat equation on~$M$ in the case where the Riemannian metric on~$M$ evolves under the Ricci flow. After motivating the problem and explaining the boundary conditions involved, we will look at how Li-Yau-type inequalities adapt to this case. Based on joint work with Mihai Bailesteanu and Xiaodong Cao.