Angenent, Sigurd B.; Knopf, Dan Precise asymptotics of the Ricci flow neckpinch. (English) Zbl 1145.53049 Commun. Anal. Geom. 15, No. 4, 773-844 (2007). Summary: 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. Cited in 22 Documents MSC: 53C44 Geometric evolution equations (mean curvature flow, Ricci flow, etc.) (MSC2010) 35K55 Nonlinear parabolic equations Keywords:finite time; Ricci flow singularity; pinching time; cylinder soliton; spectrum PDFBibTeX XMLCite \textit{S. B. Angenent} and \textit{D. Knopf}, Commun. Anal. Geom. 15, No. 4, 773--844 (2007; Zbl 1145.53049) Full Text: DOI arXiv Euclid