Calculus of Variations and Geometric Measure Theory

J. Enders - R. Buzano - P. Topping

On Type I Singularities in Ricci flow

created by muller on 12 Jun 2018
modified on 13 Jun 2022


Published Paper

Inserted: 12 jun 2018
Last Updated: 13 jun 2022

Journal: Communications in Analysis and Geometry
Volume: 19
Number: 5
Year: 2011
Doi: 10.4310/CAG.2011.v19.n5.a4

ArXiv: 1005.1624 PDF

Note name change of one author from Reto Müller to Reto Buzano in 2015. Please cite as Enders-Müller-Topping. Name changed here in order to import to author page correctly.


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.