报告题目： Metric Extension Problem under Curvature Conditions

报告摘要：: Gromov asked whether an arbitrary boundary metric on a compact manifold with boundary can always be extended to a global metric with positive scalar curvature. In this talk, I will first review the resolution of this question and its application to the non-fill-in problem, based on joint work with Prof. Yuguang Shi and Guodong Wei. Then I will discuss some recent developments regarding this metric extension problem under stronger curvature conditions, based on joint work with Jintian Zhu. We show that extensions always exist for positive Ricci curvature, but not necessarily for positive sectional curvature. For negative sectional curvature, we identify a global obstruction and prove solvability in certain cases where this obstruction vanishes.

报告人：王文龙，南开大学数学科学学院副教授。

报告时间：2025年7月13日14:30

报告地点： 修远楼A栋604

主办单位：九游会国际数学与统计学院

联系人：牟双

欢迎广大师生参加！