TY  - JOUR
A1  - Enders, Jörg
A1  - Müller, Reto
A1  - Topping, Peter M.
T1  - On Type-I singularities in Ricci flow
JF  - Communications in analysis and geometry
N2  - 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].
Y1  - 2011
SN  - 1019-8385
VL  - 19
IS  - 5
SP  - 905
EP  - 922
PB  - International Press of Boston
CY  - Somerville
ER  -