Surface projective convexe de volume fini

Ludovic Marquis (1)

1 UMPA-ENSL - Unité de Mathématiques Pures et Appliquées

A convex projective surface is the quotient of a properly convex open $\O$ of $\P$ by a discret subgroup $\G$ of $\s$. We give some caracterisations of the fact that a convex projective surface is of finite volume for the Busemann's measure. We deduce of this that if $\O$ is not a triangle then $\O$ is strictly convex, with $\Cc^1$ boundary and that a convex projective surface $S$ is of finite volume if and only if the dual surface is of finite volume.

Domaines: Topologie géométrique [math.GT]

Ludovic Marquis. Surface projective convexe de volume fini. Annales de l'Institut Fourier, 2012, 62 (1), p. 325-392. ⟨10.5802/aif.2707⟩. ⟨hal-00361030v2⟩