On Type-I singularities in Ricci flow

Joerg Enders, Reto Müller, Peter M. Topping
2011 Communications in analysis and geometry  
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
more » ... ial regularity result for mean curvature flow.
doi:10.4310/cag.2011.v19.n5.a4 fatcat:uis2c3bxsjb7toti4t53jlweem