Singular Ricci flows I

TL;DR

This paper introduces singular Ricci flows as limits of Ricci flows with surgery on 3-manifolds, establishing their properties and convergence as surgery parameters tend to zero.

Contribution

It defines singular Ricci flows, proves their existence as limits of flows with surgery, and analyzes their geometric and analytical properties.

Findings

Flow with surgery subconverges to a singular Ricci flow as surgery parameter tends to zero

Singular Ricci flows satisfy certain asymptotic conditions

The paper establishes key geometric and analytical properties of singular Ricci flows

Abstract

We introduce singular Ricci flows, which are Ricci flow spacetimes subject to certain asymptotic conditions. We consider the behavior of Ricci flow with surgery starting from a fixed initial compact Riemannian 3-manifold, as the surgery parameter varies. We prove that the flow with surgery subconverges to a singular Ricci flow as the surgery parameter tends to zero. We establish a number of geometric and analytical properties of singular Ricci flows.