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arXiv · 1005.1624

On Type I Singularities in Ricci flow

Joerg Enders·Reto Müller·Peter M. Topping
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Abstract

We define several notions of singular set for Type I Ricci flows and show that they all coincide. In order to do this, we prove that blow-ups around singular points converge to nontrivial gradient shrinking solitons, thus extending work of Naber. As a by-product we conclude that the volume of a finite-volume singular set vanishes at the singular time. We also define a notion of density for Type I Ricci flows and use it to prove a regularity theorem reminiscent of White's partial regularity result for mean curvature flow.

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Joerg Enders, Reto Müller, Peter M. Topping. 2010-05-10. On Type I Singularities in Ricci flow. https://doi.org/10.4310/cag.2011.v19.n5.a4

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