报告题目：Gromov-Hausdorff precompactness of incomplete domains with lower bounded Ricci curvature
时 间：2022年5月5日（星期四）下午15：00
地 点：腾讯会议（ID：805-584-890）
主 办：数学与统计学院, 福建省分析数学及应用重点实验室、福建师范大学数学研究中心
参加对象：相关专业师生
报告摘要：Gromov's precompactness on bounded compact metric spaces in the Gromov-Hausdorff topology has been a basis of many branches in the modern differential geometry, which leads to many applications. By Bishop-Gromov's relative volume comparison, all complete manifolds with base points and lower bounded Ricci curvature forms a precompact family equivipped with the pointed Gromov-Hausdorff topology. However, it generally fails for incomplete domains with their length metrics, even if their Ricci curvature has a uniform lower bound. For example, the Riemannian universal covers of r-balls admit no precompactness. We provide a new principle for the precompactness of such domains in a natural way. In particular, there are normal universal covers of balls that have precompactness, which fit in many geometric applications.
报告人简介： 胥世成，首都师范大学副教授，主要从事几何分析方向研究，在J. Differential Geom.、Adv. Math.、Trans. Amer. Math. Soc.、Int. Math. Res. Not.、J. Geom. Anal.、Commun. Contemp. Math.、Proc. Amer. Math. Soc.等国际权威学术期刊发表学术论文10余篇，目前主持国家自然科学基金面上项目一项，完成青年基金一项。