Manifolds with PIC1 pinched curvature

Recently it has been proved that three-dimensional complete manifolds with nonnegatively pinched Ricci curvature must be flat or compact, thus confirming a conjecture of Hamilton.We generalise our work on the existence of Ricci flows from noncompact pinched three-manifolds in order to prove a higher-dimensional analogue.We construct a solution to Ricci flow, for all time, starting with an arbitrary complete noncompact manifold that is PIC1 pinched.As an application we prove that any complete manifold of nonnegative complex sectional curvature that is PIC1 pinched must be flat or compact.53C20, 53C21, 53E20