On Type I Singularities in Ricci flow

Details On Type I Singularities in Ricci flow On Type I Singularities in Ricci flow

2010-05-10

arxiv.org/abs/1005.1624v2

Mathematics

Differential Geometry

13 pages, references added, final version, to appear in CAG

Scientific paper

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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