@article{EndersMuellerTopping2011, author = {Enders, J{\"o}rg and M{\"u}ller, Reto and Topping, Peter M.}, title = {On Type-I singularities in Ricci flow}, series = {Communications in analysis and geometry}, volume = {19}, journal = {Communications in analysis and geometry}, number = {5}, publisher = {International Press of Boston}, address = {Somerville}, issn = {1019-8385}, pages = {905 -- 922}, year = {2011}, abstract = {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 [15]. 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 [22].}, language = {en} }