# On type-I singularities in Ricci flow

@article{Enders2010OnTS,
title={On type-I singularities in Ricci flow},
author={Joerg Enders and Reto Muller and Peter M. Topping},
journal={Communications in Analysis and Geometry},
year={2010},
volume={19},
pages={905-922}
}
• Published 10 May 2010
• Mathematics
• Communications in Analysis and Geometry
We dene several notions of singular set for Type I Ricci ows 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 byproduct we conclude that the volume of a nite-volume singular set vanishes at the singular time. We also dene a notion of density for Type I Ricci ows and use it to prove a regularity theorem reminiscent of White’s partial regularity result for…
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