Canonical smoothing of compact Aleksandrov surfaces via Ricci flow
[Régularisation canonique des surfaces d'Aleksandrov compactes par le flot de Ricci]
Annales scientifiques de l'École Normale Supérieure, Série 4, Tome 51 (2018) no. 2, pp. 263-279.

Dans cet article, on montre l'existence et l'unicité du flot de Ricci avec pour condition initiale une surface d'Aleksandrov compacte à courbure minorée. Cela nécessite un affaiblissement de la notion de condition initiale permettant de considérer des espaces métriques a priori non riemanniens. Comme corollaire, on montre que le flot de Ricci d'une surface compacte dépend lissement des perturbations de sa condition initiale au sens de Gromov-Hausdorff.

In this paper, we show existence and uniqueness of Ricci flow whose initial condition is a compact Aleksandrov 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.

Publié le :
DOI : 10.24033/asens.2356
Classification : 53C44, 53C45
Keywords: Ricci flow, Aleksandrov surfaces whose curvature is bounded from below
Mot clés : Flot de Ricci, surfaces d'Aleksandrov à courbure minorée 
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     volume = {Ser. 4, 51},
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Richard, Thomas. Canonical smoothing of compact Aleksandrov surfaces via Ricci flow. Annales scientifiques de l'École Normale Supérieure, Série 4, Tome 51 (2018) no. 2, pp. 263-279. doi : 10.24033/asens.2356. http://www.numdam.org/articles/10.24033/asens.2356/

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