We investigates a class of n-dimensional Ricci flows with non-negative
Ricci curvature start from metric cones which are Reifenberg outside the tip. We show that any such flow is a self-similar solution locally in space up to an exponential error in time. As an application, we show that smooth n-dimensional, complete non-compact uniformly PIC1-pinched Riemannian manifolds with positive asymptotic volume ratio are Euclidean, thus confirming a higher dimensional version of a conjecture of Hamilton and Lott in a non-collapsed setting. It also reproves the original conjecture due to Hamilton and Lott in three dimensions. This is joint work with F. Schulze and M. Simon.
