Communications in Analysis and Geometry

Volume 15 (2007)

Number 4

Precise asymptotics of the Ricci flow neckpinch

Pages: 773 – 844



Sigurd B. Angenent

Dan Knopf


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.

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