Ricci Flow Emerging from Rotationally Symmetric Degenerate Neckpinches

Abstract

In previous work, Angenent, Isenberg, and Knopf created type-II Ricci flow neckpinch singularities. In this paper we construct solutions to Ricci flow whose initial data is the singular metric resulting from these singularities. We show in particular that the curvature decreases at the same rate at which it blew up. This is the first example of Ricci flow starting from a type-II singularity.

References in corpus (1)

• Formal matched asymptotics for degenerate Ricci flow neckpinches

Cited by in corpus (2)

• Ricci Solitons, Conical Singularities, and Nonuniqueness
• A numerical stability analysis of mean curvature flow of noncompact hypersurfaces with Type-II curvature blowup