2 citations · 2 across the 1 of their papers we have counts for
4 papers
Curvature bounds via Ricci smoothing
Vitali Kapovitch
We give a proof of the fact that the upper and the lower sectional curvature bounds of a complete manifold vary at a bounded rate under the Ricci flow.
Restrictions on collapsing with a lower sectional curvature bound
Vitali Kapovitch
We obtain new topological information about the local structure of collapsing under a lower sectional curvature bound. As an application we prove a new sphere theorem and obtain a…
Finiteness theorems for nonnegatively curved vector bundles
Igor Belegradek, Vitali Kapovitch
We prove several finiteness theorems for the normal bundles to souls in nonnegatively curved manifolds. More generally, we obtain finiteness results for open Riemannian manifolds w…
Topological obstructions to nonnegative curvature
Igor Belegradek, Vitali Kapovitch
We find new obstructions to the existence of complete Riemannian metric of nonnegative sectional curvature on manifolds with infinite fundamental groups. In particular, we construc…