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Convergence of Ricci flows with bounded scalar curvature. (English) Zbl 1410.53063
Summary: 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 $$\geq 4$$. In the course of the proof, we will also establish $$L^{p<2}$$-curvature bounds on time-slices of such flows.

MSC:
 53C44 Geometric evolution equations (mean curvature flow, Ricci flow, etc.) (MSC2010) 53C23 Global geometric and topological methods (à la Gromov); differential geometric analysis on metric spaces 53C56 Other complex differential geometry
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