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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 set of codimension $geq 4$. The result has two main consequences: First, it implies that singularities in Ricci flows with bounded scalar curvature have codimension $geq 4$ and, second, it establishes a general form of the Hamilton-Tian Conjecture, which is even true in the Riemannian case. In the course of the proof, we will also establish the following results: $L^{p < 4}$ curvature bounds, integral bounds on the curvature radius, Gromov-Hausdorff closeness of time-slices, an $varepsilon$-regularity theorem for Ricci flows and an improved backwards pseudolocality theorem.
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
In this paper we analyze the behavior of the distance function under Ricci flows whose scalar curvature is uniformly bounded. We will show that on small time-intervals the distance function is $frac12$-Holder continuous in a uniform sense. This impli
We prove a parametrized compactness theorem on manifolds of bounded Ricci curvature, upper bounded diameter and lower bounded injectivity radius.
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 su
We employ three different methods to prove the following result on prescribed scalar curvature plus mean curvature problem: Let $(M^n,g_0)$ be a $n$-dimensional smooth compact manifold with boundary, where $n geq 3$, assume the conformal invariant $Y