Convergence of Ricci flows with bounded scalar curvature

• 成果类型: Article
• 署名作者: Bamler, Richard H.
• 刊物名称: ANNALS OF MATHEMATICS
• ISSN/ISSBN: 0003-486X
• DOI: 10.4007/annals.2018.188.3.2
• 发表日期: 2018
• 页码: 753-831
• 关键词: kahler-einstein metrics; quantitative stratification; compactness theorem; REGULARITY; SINGULARITIES; MANIFOLDS; RIGIDITY; SPACES; LIMITS

摘要

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 >= 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 >= 4. In the course of the proof, we will also establish L-P <2-curvature bounds on time-slices of such flows.