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Regularity theory for Type I Ricci flows

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Panagiotis Gianniotis
University of Waterloo/University of Toronto
Tue, 2017-09-19 17:00 - 17:30
MPIM Lecture Hall

A  Ricci flow exhibits a Type I singularity if the curvature blows up at a certain rate near the singular time. Type I singularities are abundant and in fact it is conjectured that they are the generic singular behaviour for the Ricci flow on closed manifolds.

In this talk, I will describe some new integral curvature estimates for Type I flows, valid up to the singular time. These estimates partially extend to higher dimensions an estimate that was recently shown to hold in dimension three by Kleiner-Lott, using Ricci flow with surgery.

In this work we use the monotonicity formula available for Type I Ricci flows, adapting the technique of quantitative stratification of Cheeger-Naber to this setting.

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