Convergence of Ricci flows with bounded scalar curvature

Understand

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 $\geq 4$.
• We also establish a general form of the Hamilton-Tian Conjecture, which is even true in the Riemannian case.
• These results are based on a compactness theorem for Ricci flows with bounded scalar curvature, which states that any sequence of such Ricci flows converges, after passing to a subsequence, to a metric space that is smooth away from a set of codimension $\geq 4$.