中科院数学与系统科学研究院
数学研究所
偏微分方程研讨班
报告人： 简旺健 博士(华罗庚数学中心)
题 目：Diameter and Ricci curvature estimates for the collapsing long-time solution of the Kahler-Ricci flow
时 间：2021.03.04（星期四）, 14:30-16:30
地 点：数学院南楼N208室
摘 要：We will first briefly recall the background of the Kahler-Ricci flow. Then we will introduce the set-up of collapsing long-time solution of the Kahler-Ricci flow, and recall some previous results. Next, we will recall the recent results of Bamler, which use the Nash entropy to control the volume of balls along Ricci flow. Using Bamler's theory, we show how to reprove Tian-Zhang's relative volume comparison estimate. Then we will show that Bamler's results are also useful in long-time solution of the Kahler-Ricci flow without Ricci curvature bound assumption. Finally, if time permits, we will show how to apply iteration process to obtain the local Ricci bound if the Kodaira dim of the manifold is one.
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