Formal matched asymptotics for degenerate Ricci flow neckpinches

TL;DR

This paper predicts detailed asymptotic behavior and curvature blow-up rates for Type-II Ricci flow singularities on rotationally symmetric spheres, extending understanding of degenerating neckpinch formations.

Contribution

It introduces a formal matched asymptotics approach to describe the asymptotic profile and blow-up rate of Ricci flow neckpinches, building on prior existence results.

Findings

Predicted detailed asymptotic profile of Ricci flow neckpinches

Estimated rate of curvature blow-up during singularity formation

Provided plausibility arguments supporting the asymptotic descriptions

Abstract

Gu and Zhu have shown that Type-II Ricci flow singularities develop from nongeneric rotationally symmetric Riemannian metrics on $S^m$, for all $m\geq 3$. In this paper, we describe and provide plausibility arguments for a detailed asymptotic profile and rate of curvature blow-up that we predict such solutions exhibit.