Strong Uniqueness of the Ricci Flow

In this paper, we derive some local a priori estimates for Ricci flow. This gives rise to some strong uniqueness theorems. As a corollary, let $g(t)$ be a smooth complete solution to the Ricci flow on ${\mathbb{R}}^3$, with the canonical Euclidean metric $E$ as initial data, then $g(t)$ is trivial, i.e. $g(t)\equiv E$.