Compactness theory of the space of Super Ricci flows

Abstract

We develop a compactness theory for super Ricci flows, which lays the foundations for the partial regularity theory in [Bam20b]. 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.

117 pages; minor corrections; Comments and questions welcome

References in corpus (1)

• A Bochner Formula on Path Space for the Ricci Flow

Cited by in corpus (9)

• Perelman-type no breather theorem for noncompact Ricci flows
• On a dichotomy of the curvature decay of steady Ricci soliton
• O(2)-symmetry of 3D steady gradient Ricci solitons
• Rigidity of spherical product Ricci solitons
• Lectures on mean curvature flow of surfaces
• Ricci flow with bounded curvature integrals
• On the improved no-local-collapsing theorem of Ricci flow
• Liouville theorems for harmonic map heat flow along ancient super Ricci flow via reduced geometry
• Kähler Soliton Surfaces Are Generically Toric