English

On the blow-up of four dimensional Ricci flow singularities

Differential Geometry 2012-04-27 v1 Analysis of PDEs

Abstract

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 \CP1\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.

Keywords

Cite

@article{arxiv.1204.5967,
  title  = {On the blow-up of four dimensional Ricci flow singularities},
  author = {Davi Máximo},
  journal= {arXiv preprint arXiv:1204.5967},
  year   = {2012}
}