Collapsed Manifolds With Ricci Bounded Covering Geometry

Abstract

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.

Cited by in corpus (4)

• Mixed curvature almost flat manifolds
• A New Proof of the Gromov's Theorem on Almost Flat Manifolds
• Fibrations, and stability for compact group actions on manifolds with local bounded Ricci covering geometry
• Small curvature concentration and Ricci flow smoothing