Canonical smoothing of compact Alexandrov surfaces via Ricci flow

Thomas Richard (1)

1 IF - Institut Fourier

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.

Mots clés: Ricci flow; Alexandrov surfaces; metric geometry

Domaines: Géométrie différentielle [math.DG]

Thomas Richard. Canonical smoothing of compact Alexandrov surfaces via Ricci flow. 2012. ⟨hal-00690909⟩