Calculus of Variations and Geometric Measure Theory
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J. Enders - R. Müller - Peter M. Topping

On Type I Singularities in Ricci flow

created by muller on 18 May 2010
modified on 12 Jun 2018

[BibTeX]

Published Paper

Inserted: 18 may 2010
Last Updated: 12 jun 2018

Journal: Commun. Anal. Geom.
Volume: 19
Number: 5
Pages: 905-922
Year: 2011

ArXiv: 1005.1624 PDF

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. 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.


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