Stability of pure Nilpotent Structures on collapsed Manifolds
报 告 人:: 胥世成
报告地点:: 综合教学楼248室
报告时间:: 2018年08月13日星期一16:00-17:00

Collapsed manifolds with bounded sectional curvature (i.e., |sec|<1 and volume of every unit ball small) are characterized by Cheeger-Fukaya-Gromov's nilpotent structures. We focus on the stability problem on pure nilpotent structures.

We prove that if two metrics on a $n$-manifold of bounded sectional curvature are $L_0$-bi-Lipchitz equivalent and sufficient collapsed (depending on $L_0$ and $n$), then up to a diffeomorphism, the underlying nilpotent Killing structures coincide with each other or one is embedded into another as a subsheaf.

It improves Cheeger-Fukaya-Gromov's locally compatibility of pure nilpotent Killing structures for one collapsed metric of bounded sectional curvature to two Lipschitz equivalent metrics. As an application, we prove that those pure nilpotent Killing structures constructed by various smoothing method to a Lipschitz equivalent $\epsilon$-collapsed metric of bounded sectional curvature are uniquely determined by the original metric modulo a diffeomorphism.


发 布 人:吴双 发布时间: 2018-08-05
作者简介:胥世成,首都师范大学数学科学学院工作。近几年来一直从事黎曼几何、黎曼流形的收敛和坍缩、和Alexandrov 空间几何、Cheeger-Colding 理论的研究,目前已经在Adv. Math, J. Differ. Geom, Trans. Amer. Math. Soc.等杂志上发表论文。