Communications in Analysis and Geometry
Volume 19 (2011)
On Type-I singularities in Ricci flow
Pages: 905 – 922
We define several notions of singular set for Type-I Ricci flows andshow that they all coincide. In order to do this, we prove thatblow-ups around singular points converge to nontrivialgradient shrinking solitons, thus extending work of Naber.As a by-product we conclude that the volume of afinite-volume singular set vanishes at the singular time.
We also define a notion of density for Type-I Ricci flows and use itto prove a regularity theorem reminiscent of White’s partialregularity result for mean curvature flow.