Convergence theorems on collapsed limit spaces under bounded Ricci curvature.

讲座时间 Datetime: 2022年6月27日，星期一，10:00—11:30

地点 Venue: 腾讯线上会议：671-471-896

主持人 Host：魏国栋

报告人 Speaker: 胥世成

单位 Affiliation:首都师范大学

报告摘要 Abstract:

One of the fundamental tools in the modern geometry is the Cheeger-Gromov’s convergence theorem in 1970-80s, which says that manifolds with bounded sectional curvature and positive injectivity radius is precompact under C^(1,α)-topology. In 1990 Anderson extend it to manifolds with bounded Ricci curvature and positive injectivity radius.

Around 1987-1992 Cheeger-Gromov and Fukaya also developed the theory on the structure of collapsed (i.e. inj. radius small) manifolds with bounded sectional curvature as well as their limit spaces.

We extend the C^(1,α)-convergence theorems to regular limit spaces of collapsed manifolds with bounded Ricci curvature and local covering geometry. As an application we give an optimal generalization of the collapsing fibration on collapsed manifolds with bounded Ricci curvature to regular limit spaces. This is a joint work with Z. Jiang and L. Kong.