Precise asymptotics of the Ricci flow neckpinch

TL;DR

This paper derives precise asymptotic descriptions of neckpinch singularities in Ricci flow, especially for rotationally symmetric cases, and compares them with formal asymptotics for more general scenarios.

Contribution

It provides the first rigorous asymptotic analysis of Ricci flow neckpinch singularities and extends the understanding beyond symmetric cases.

Findings

Established precise asymptotics for rotationally symmetric neckpinches.

Compared rigorous results with formal asymptotics for general neckpinches.

Enhanced understanding of singularity formation in Ricci flow.

Abstract

The best known finite-time local Ricci flow singularity is the neckpinch, in which a proper subset of the manifold becomes geometrically close to a portion of a shrinking cylinder. In this paper, we prove precise asymptotics for rotationally symmetric Ricci flow neckpinches. We then compare these rigorous results with formal matched asymptotics for fully general neckpinch singularities.