# On the blow-up of four dimensional Ricci flow singularities

```@article{Maximo2012OnTB,
title={On the blow-up of four dimensional Ricci flow singularities},
author={Davi M'aximo},
journal={arXiv: Differential Geometry},
year={2012}
}```
• Davi M'aximo
• Published 2012
• Mathematics
• arXiv: Differential Geometry
In this paper we prove a conjecture by Feldman-Ilmanen-Knopf in \cite{FIK} that the gradient shrinking soliton metric they constructed on the tautological line bundle over \$\CP^1\$ is the uniform limit of blow-ups of a type I Ricci flow singularity on a closed manifold. We use this result to show that limits of blow-ups of Ricci flow singularities on closed four dimensional manifolds do not necessarily have non-negative Ricci curvature.
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