On the structure of noncollapsed Ricci flow limit spaces

Abstract

We establish a weak compactness theorem for the moduli space of closed Ricci flows, each equipped with a natural spacetime distance, under pointed Gromov--Hausdorff convergence. For the subspace of flows with uniformly bounded entropy, we further develop a structure theory for the corresponding noncollapsed Ricci flow limit spaces, showing that the regular part, where convergence is smooth, admits the structure of a Ricci flow spacetime, while the singular set has codimension at least four.

arXiv commentRevised version. By modifying the spacetime distance, we extend the weak compactness theorem to the possibly collapsing setting. The main structure theorems for noncollapsed Ricci flow limit spaces remain unchanged. We also correct several typos.134 pages, 1 figure