Precompactness of domains with lower Ricci curvature bound under Gromov-Hausdorff topology
科研大讨论系列报告
报告题目(Title)：Precompactness of domains with lower Ricci curvature bound under Gromov-Hausdorff topology
报告人(Speaker)：胥世成（首都师范大学教授）
地点(Place)：北京师范大学后主楼1225
时间(Time)：2024年3月22日(周五)，下午4:00-5:00
邀请人(Inviter)：黄红
报告摘要
Based on a quantitative version of the classical Hopf-Rinow theorem in terms of the doubling property, we prove new precompactness principles in the (pointed) Gromov-Hausdorff topology for domains in (maybe incomplete) Riemannian manifolds with a lower Ricci curvature bound, which are applicable to those domain with weak regularities considered in PDE theory, and the covering spaces of balls naturally appear in the study of local geometry and topology of manifolds with lower curvature bounds. All the new principles are more general than those earlier known for manifolds with smooth boundary, and improves those for manifolds with non-smooth boundary. They are also readily applicable to some problems in Geometry via PDE.
