Collapsed Manifolds With Ricci Bounded Covering Geometry
Differential Geometry
2018-08-14 v1
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.
Cite
@article{arxiv.1808.03774,
title = {Collapsed Manifolds With Ricci Bounded Covering Geometry},
author = {Hongzhi Huang and Lingling Kong and Xiaochun Rong and Shicheng Xu},
journal= {arXiv preprint arXiv:1808.03774},
year = {2018}
}