Uniqueness of weak solutions for the normalised Ricci flow in two dimensions

Abstract

We show uniqueness of classical solutions of the normalised two-dimensional HamiltonRicci flow on closed, smooth manifolds for smooth data among solutions satisfying (essentially) only a uniform bound for the Liouville energy and a natural space-time L 2 -bound for the time derivative of the solution. The result is surprising when compared with results for the harmonic map heat flow, where non-uniqueness through reverse bubbling may occur.