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Precise asymptotics of the Ricci flow neckpinch. (English) Zbl 1145.53049

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.

MSC:

53C44 Geometric evolution equations (mean curvature flow, Ricci flow, etc.) (MSC2010)
35K55 Nonlinear parabolic equations
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