Fill-in with nonnegative scalar curvature
几何分析专题报告
报告题目(Title)：Fill-in with nonnegative scalar curvature
报告人(Speaker)：王文龙 (南开大学)
地点(Place)：ZOOM ID & PWD：64430742724；123456/61358944513；123456
时间(Time)：2021年3月13日 9:00-11:00/3月16日8:30-10:30
邀请人(Inviter)：熊金钢
报告摘要
In the first talk, we will first introduce the notion “fill-in with nonnegative scalar curvature”. Then we will talk about the motivation of this fill-in problem both from geometry of compact manifold with boundary and quasi-local mass. In the end, we will review some relevant classical results and new questions raised mainly by Gromov. In the second talk, we will focus on our answer to an open problem and partial answers to two conjectures by Gromov. Precisely, we will first prove the extensibility of an arbitrary boundary metric to a positive scalar curvature metric inside for a compact manifold with boundary. Then we will introduce a fill-in invariant and discuss its relationship with the positive mass theorems for asymptotically flat (AF) and asymptotically hyperbolic (AH) manifolds. In particular, we will prove that the positive mass theorem for AH manifolds implies that for AF manifolds. In the end, we will give some estimates for the fill-in invariant. The second talk is based on joint works with Prof. Yuguang Shi, Dr. Guodong Wei and Jintian Zhu.
