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Minimally invasive surgery for Ricci flow singularities. (English) Zbl 1258.53066

This paper is motivated by Perelman’s construction of a Ricci flow with surgery for closed Riemannian 3-manifolds. It is hoped that one can flow directly from the singularity without having to perform a surgery that involves arbitrary choices of parameters. This hope is confirmed in the present paper in the case of rotationally symmetric neckpinches on the \(n\)-sphere. While the question of uniqueness is left open, it is proved that the resulting solution has unique asymptotic profile.

MSC:

53C44 Geometric evolution equations (mean curvature flow, Ricci flow, etc.) (MSC2010)
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