Collapsed manifolds with Ricci bounded covering geometry
Hongzhi Huang, Lingling Kong, Xiaochun Rong, Shicheng Xu
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. Applying the techniques in the Ricci flow, we partially extend the nilpotent structural results of Cheeger-Fukaya-Gromov, on the collapsed manifolds with (sectional curvature) local bounded covering geometry, to the manifolds with (global) Ricci bounded covering geometry.
Topics & Concepts
MathematicsRicci flowRicci curvatureCurvature of Riemannian manifoldsBounded functionSectional curvatureRiemannian geometryGeometryRicci-flat manifoldPure mathematicsCover (algebra)CurvatureMathematical analysisScalar curvatureEngineeringMechanical engineeringGeometric Analysis and Curvature FlowsGeometry and complex manifoldsGeometric and Algebraic Topology