On Type I Singularities in Ricci flow
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 blowups around singular points converge to nontrivial gradient shrinking solitons, thus extending work of Naber. As a byproduct we conclude that the volume of a finitevolume 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.
 Publication:

arXiv eprints
 Pub Date:
 May 2010
 DOI:
 10.48550/arXiv.1005.1624
 arXiv:
 arXiv:1005.1624
 Bibcode:
 2010arXiv1005.1624E
 Keywords:

 Mathematics  Differential Geometry
 EPrint:
 13 pages, references added, final version, to appear in CAG