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

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 ${\int }_0^T\sqrt{T-t}R(p_0,t)dt<\infty$ for some point $p_0$. This partially confirms a conjecture of Perelman.