3 papers
math.DG2022
Canonical nilpotent structure under bounded Ricci curvature and Reifenberg local covering geometry over regular limits
Zuohai Jiang, Lingling Kong, Shicheng Xu
It is known that a closed collapsed Riemannian -manifold of bounded Ricci curvature and Reifenberg local covering geometry admits a nilpotent structure in the sense of C…
math.DG2022
Convergence of Ricci-limit spaces under bounded Ricci curvature and local covering geometry I
Zuohai Jiang, Lingling Kong, Shicheng Xu
We extend Cheeger-Gromov's and Anderson's convergence theorems to regular limit spaces of manifolds with bounded Ricci curvature and local covering geometry, by establishing the $C…
math.DG2018
Stability of pure Nilpotent Structures on collapsed Manifolds
Zuohai Jiang, Shicheng Xu
The goal of this paper is to study the stability of pure nilpotent structures on a manifold associated to different collapsed metrics. We prove that if two metrics on a -manifol…