We study collapsed manifolds with Ricci bounded covering geometry i.e., Ricci curvature is bounded below and the Riemannian universal cover is non-collapsed or consists of uniform Reifenberg points. Via Ricci flows' techniques, we partially extend the nilpotent structural results of Cheeger-Fukaya-Gromov, on collapsed manifolds with (sectional curvature) local bounded covering geometry, to manifolds with (global) Ricci boundedcovering geometry.

中文翻译：

---

具有 Ricci 有界覆盖几何的折叠流形

我们研究了具有 Ricci 有界覆盖几何的塌陷流形，即 Ricci 曲率有界，黎曼通用覆盖是非塌陷的或由均匀的 Reifenberg 点组成。通过 Ricci 流的技术，我们将 Cheeger-Fukaya-Gromov 的幂零结构结果在具有（截面曲率）局部有界覆盖几何的塌陷流形上部分扩展到具有（全局）Ricci 有界覆盖几何的流形。