Convergence of Ricci flows with bounded scalar curvature

By Richard Bamler. 2016

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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.

Subfields: Applied Mathematics, Astronomy and Astrophysics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/174e2e0b8132365892a30b184a7a349c1539ec82

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In Applied Mathematics

In Astronomy and Astrophysics

In Geometry and Topology

Citations in the corpus

The Kähler–Ricci flow and optimal degenerations (2016, background): “2) in terms of Φt, and the fact that the singular set has codimension at least 4 [1], and so in particular we can choose K with the volume of Y \ K being arbitrarily small.”