Uniqueness of Ricci flows from non‐atomic Radon measures on Riemann surfaces

In previous work (Topping and Yin, https://arxiv.org/abs/2107.14686 ), we established the existence of a Ricci flow starting with a Riemann surface coupled with a non‐atomic Radon measure as a conformal factor. In this paper, we prove uniqueness, settling Conjecture 1.3 of Topping and Yin ( https://arxiv.org/abs/2107.14686 ). Combining these two works yields a canonical smoothing of such rough surfaces that also regularises their geometry at infinity.