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We develop a compactness theory for super Ricci flows, which lays the foundations for the partial regularity theory in [Bam20b]. Our results imply that any sequence of super Ricci flows of the same dimension that is pointed in an appropriate sense subsequentially converges to a certain type of synthetic flow, called a metric flow. We will study the geometric and analytic properties of this limiting flow, as well as the convergence in detail. We will also see that, under appropriate local curvature bounds, a limit of Ricci flows can be decomposed into a regular and singular part. The regular part can be endowed with a canonical structure of a Ricci flow spacetime and we have smooth convergence on a certain subset of the regular part.
In this paper we characterize non-collapsed limits of Ricci flows. We show that such limits are smooth away from a set of codimension $geq 4$ in the parabolic sense and that the tangent flows at every point are given by gradient shrinking solitons, p
In this paper we prove a compactness result for Ricci flows with bounded scalar curvature and entropy. It states that given any sequence of such Ricci flows, we can pass to a subsequence that converges to a metric space which is smooth away from a se
In this article, we study the Ricci flow neckpinch in the context of metric measure spaces. We introduce the notion of a Ricci flow metric measure spacetime and of a weak (refined) super Ricci flow associated to convex cost functions (cost functions
This is a survey on recent developments in Ricci flows.
In this paper we prove convergence and compactness results for Ricci flows with bounded scalar curvature and entropy. More specifically, we show that Ricci flows with bounded scalar curvature converge smoothly away from a singular set of codimension