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In this paper, we show existence and uniqueness of Ricci flow whose initialcondition is a compact Alexandrov surface with curvature bounded from below.This requires a weakening of the notion of initial condition which is able todeal with a priori non-Riemannian metric spaces. As a by-product, we obtainthat the Ricci flow of a surface depends smoothly on Gromov-Hausdorffperturbations of the initial condition.

Canonical smoothing of compact Alexandrov surfaces via Ricci flow