On the blow-up of four dimensional Ricci flow singularities

2012/04/26 by Máximo, Davi
#Analysis of PDEs (math.AP) #Differential Geometry (math.DG) #FOS: Mathematics

paper · doi:10.48550/arxiv.1204.5967

Abstract

In this paper we prove a conjecture by Feldman-Ilmanen-Knopf in \citeFIK that the gradient shrinking soliton metric they constructed on the tautological line bundle over \CP¹ 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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