报告题目：Metric Extension Problem under Curvature Conditions

主讲人：王文龙

摘要：Gromov asked whether every smooth metric on the boundary of a compact manifold extends to a metric of positive scalar curvature on the whole manifold. 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. I will then discuss recent progress on the metric extension problem under stronger curvature conditions, based on joint work with Jintian Zhu. We prove that extensions exist with any prescribed positive lower bound for Ricci curvature, but may fail to exist under positive sectional curvature. For negative sectional curvature, we identify a global obstruction and prove solvability for a class of manifolds. This class includes handlebodies and disk bundles over closed negatively curved manifolds and is closed under boundary connected sums.

主讲人简介：王文龙，南开大学数学学院教授、博士生导师，国家“四青”人才。本科就读于南开大学，博士毕业于北京大学数学系，公派赴华盛顿大学联合培养。研究方向是几何分析，包括与数量曲率和广义相对论中质量有关的几何问题、几何背景PDE 的刚性定理和内估计、预定曲率填充问题等。文章发表在J. Reine Angew. Math., Math. Ann., Int. Math. Res. Not.等国际权威数学期刊。

邀请人：李刚 数学学院副教授

时间：2026年11月4日（周三）上午10：00-11：00

地点：中心校区知新楼B座1032