Surface projective convexe de volume fini

Details Surface projective convexe de volume fini Surface projective convexe de volume fini

2009-02-18

arxiv.org/abs/0902.3143v2

Mathematics

Geometric Topology

To be publish in: Annales de l'Institut Fourier

Scientific paper

A convex projective surface is the quotient of a properly convex open $\Omega$ of $\mathbb{P}(\R)$ by a discret subgroup $\Gamma$ of $\mathrm{SL}_3(\R)$. 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 $\Omega$ is not a triangle then $\Omega$ 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.

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