Communications in Analysis and Geometry
Volume 15 (2007)
Precise asymptotics of the Ricci flow neckpinch
Pages: 773 – 844
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.