A lower bound for the scalar curvature of the standard solution of the Ricci flow

Abstract

In this paper we will give a rigorous proof of the lower bound for the scalar curvature of the standard solution of the Ricci flow conjectured by G. Perelman. We will prove that the scalar curvature $R$ of the standard solution satisfies $R(x,t)\ge C_0/(1-t)\quad\forall x\in\Bbb{R}^3,0\le t<1$, for some constant $C_0>0$.