Dimension reduction under the Ricci flow on manifolds with nonnegative curvature operator

Abstract

In this paper, we study the dilation limit of solutions to the Ricci flow on manifolds with nonnegative curvature operator. We first show that such a dilation limit must be a product of a compact ancient Type I solution of the Ricci flow with flat factors. Then we show that, under the Type I normalized Ricci flow, the compact factor has a subsequence converging to a Ricci soliton.