Canonical smoothing of compact Alexandrov surfaces via Ricci flow

Mathematics – Differential Geometry

Scientific paper

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12 pages

Scientific paper

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

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