24 citations · 71 across the 20 of their papers we have counts for
21 papers
Gromov-Hausdorff Limits of Aspherical Manifolds
Xiaochun Rong
Let be a compact Gromov-Hausdorff limit space of a collapsing sequence of compact -manifolds, , of Ricci curvature and all points in …
Open Alexandrov spaces of nonnegative curvature
Xueping Li, Xiaochun Rong
Let be an open (i.e. complete, non-compact and without boundary) Alexandrov -space of nonnegative curvature with a soul . In this paper, we will establish several structu…
Quantitative Maximal Diameter Rigidity of Positive Ricci Curvature
Tianyin Ren, Xiaochun Rong
In Riemannian geometry, the Cheng's maximal diameter rigidity theorem says that if a complete -manifold of Ricci curvature, , has the maximal…
Collapsed manifolds with local Ricci bounded covering geometry
Xiaochun Rong
For , we say that an -manifold satisfies local -bound Ricci covering geometry, if Ricci curvature , and for all , $\text{vol}(…
Collapsing geometry with Ricci curvature bounded below and Ricci flow smoothing
Shaosai Huang, Xiaochun Rong, Bing Wang
We survey some recent developments in the study of collapsing Riemannian manifolds with Ricci curvature bounded below, especially the locally bounded Ricci covering geometry and th…
A Generalized -Diffeomorphism Finiteness Theorem
Xiaochun Rong, Xuchao Yao
The -diffeomorphism finiteness result (\cite{FR1,2}, \cite{PT}) asserts that the diffeomorphic types of compact -manifolds with vanishing first and second homotopy grou…