Formal matched asymptotics for degenerate Ricci flow neckpinches

Abstract

Gu and Zhu have shown that Type-II Ricci flow singularities develop from nongeneric rotationally symmetric Riemannian metrics on $S^m$, for all $m\ge 3$. 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.

References in corpus (2)

• Notes on Perelman's papers
• The Modelling of Degenerate Neck Pinch Singularities in Ricci Flow by Bryant Solitons

Cited by in corpus (6)

• Simplicial Ricci Flow
• Universality in mean curvature flow neckpinches
• Topological Signals of Singularities in Ricci Flow
• Ricci Flow Emerging from Rotationally Symmetric Degenerate Neckpinches
• Nonlinear systems of PDEs admitting infinite-dimensional Lie algebras and their connection with Ricci flows. II: The two-dimensional space case
• A numerical stability analysis of mean curvature flow of noncompact hypersurfaces with Type-II curvature blowup