Strong Uniqueness of the Ricci Flow

Abstract

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. $g(t)\equiv E$.

21 pages

Cited by in corpus (8)

• Recent Progress on Ricci Solitons
• Sharp logarithmic Sobolev inequalities on gradient solitons and applications
• Perelman's reduced volume and a gap theorem for the Ricci flow
• Backwards uniqueness of the Ricci flow
• Existence and applications of Ricci flows via pseudolocality
• On complete gradient shrinking Ricci solitons
• Singularities of Connection Ricci Flow and Ricci Harmonic Flow
• On the asymptotic reduced volume of the Ricci flow