On the $\kappa-$solutions of the Ricci flow on noncompact 3-manifolds

Liang Cheng; Anqiang Zhu

On the $\kappa-$solutions of the Ricci flow on noncompact 3-manifolds

Differential Geometry 2018-10-23 v1

Authors: Liang Cheng , Anqiang Zhu

Abstract

In this paper we prove that there is no $\kappa$ -solution of Ricci flow on 3-dimensional noncompact manifold with strictly positive sectional curvature and blow up at some finite time $T$ satisfying $\int^T_0 \sqrt{T-t} R(p_0,t)dt< \infty$ for some point $p_0$ . This partially confirms a conjecture of Perelman.

Keywords

Ricci flow kappa-solution noncompact 3-manifold sectional curvature Perelman conjecture

Cite

@article{arxiv.1810.08934,
  title  = {On the $\kappa-$solutions of the Ricci flow on noncompact 3-manifolds},
  author = {Liang Cheng and Anqiang Zhu},
  journal= {arXiv preprint arXiv:1810.08934},
  year   = {2018}
}

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