题目：Metric Extension Problem under Curvature Conditions

报告人：王文龙 副教授（南开大学）

地点：宁静楼104室

时间：2025年6月4日 15:00-16:00

Abstract: 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.

报告人简介：王文龙，南开大学数学学院副教授。研究方向为几何分析，相关成果发表在Crelle,  Math. Ann. , IMRN等国外著名学术期刊。

欢迎各位参加！