Diameter and Ricci curvature estimates for the long-time solution of the Kahler-Ricci flow

Tecent Meeting ID: 549 385 974 

Abstract:

We will start with Bamler's first paper of the recent three preprints. First, we will introduce the notions of Wasserstein distance, variance, and the Nash entropy and how to use the Nash entropy to bound the volume of balls. Then we will show how to use these entropy bounds to reprove Tian-Zhang's relative volume comparison result. Next, we will consider the collapsing long-time solution of Kahler-Ricci flow on minimal models, and show that Bamler's tools are also useful in this situation even without Ricci curvature bound. Finally, we will show how to apply iteration process to obtain the local Ricci bound if the Kodaira dim of the manifold is one.