题目：Total Mean Curvature of Nonnegative Scalar Curvature Fill-ins

摘要：We first prove the extensibility of an arbitrary boundary metric to a positive scalar curvature metric inside for a compact manifold with boundary, which solves an open problem due to Gromov. Then we 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 prove that the positive mass theorem for AH manifolds implies that for AF manifolds. In the end, we give some estimates for the fill-in invariant, which provide some partially affirmative answers to two conjectures by Gromov. This is joint work with Prof. Yuguang Shi and Dr. Guodong Wei.

报告人：王文龙

报告人简介：王文龙，2017年博士毕业于北京大学数学系，北京国际数学研究中心博士后，2019年起在南开大学数学学院工作。主要研究领域是几何分析与微分几何。近几年有一系列关于带边流形内部正数量曲率填充问题(与正质量定理密切相关)的出色工作。

时间：2020年11月27日，星期五，10:00-11:00

地点：腾讯会议，会议ID：249 585 864

点击链接入会，或添加至会议列表：https://meeting.tencent.com/s/PidIcBDTGShf

邀请人：李刚