On the blow-up of four dimensional Ricci flow singularities

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

2012-04-26

arxiv.org/abs/1204.5967v1

Mathematics

Differential Geometry

Scientific paper

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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