On Type I Singularities in Ricci flow

Understand

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.