Compactness theory of the space of Super Ricci flows

• 成果类型: Article
• 署名作者: Bamler, Richard H.
• 署名单位: University of California System; University of California Berkeley
• 刊物名称: INVENTIONES MATHEMATICAE
• ISSN/ISSBN: 0020-9910
• DOI: 10.1007/s00222-023-01196-3
• 发表日期: 2023
• 页码: 1121-1277
• 关键词: metric-measure-spaces; CURVATURE; geometry; bounds; inequalities; REGULARITY; MANIFOLDS; PROPERTY; RIGIDITY

摘要

We develop a compactness theory for super Ricci flows, which lays the foundations for the partial regularity theory in Bamler (Structure Theory of Non-collapsed Limits of Ricci Flows, , 2020). Our results imply that any sequence of super Ricci flows of the same dimension that is pointed in an appropriate sense subsequentially converges to a certain type of synthetic flow, called a metric flow. We will study the geometric and analytic properties of this limiting flow, as well as the convergence in detail. We will also see that, under appropriate local curvature bounds, a limit of Ricci flows can be decomposed into a regular and singular part. The regular part can be endowed with a canonical structure of a Ricci flow spacetime and we have smooth convergence on a certain subset of the regular part.