Surface Projective Convexe de volume fini  [ Convex projective surface of finite volume ]
Annales de l'Institut Fourier, Volume 62 (2012) no. 1, p. 325-392

A convex projective surface is the quotient of a properly convex open Ω of the projective real space 2 () by a discrete subgroup Γ of SL 3 (). We give some caracterisations of the fact that a convex projective surface is of finite volume for the Busemann’s measure. We deduce that, if Ω is not a triangle, then Ω is strictly convex, with 𝒞 1 boundary and that a convex projective surface S is of finite volume if and only if the dual surface is of finite volume.

Une surface projective convexe est le quotient d’un ouvert proprement convexe Ω de l’espace projectif réel 2 () par un sous-groupe discret Γ de SL 3 (). Nous donnons plusieurs caractérisations du fait qu’une surface projective convexe est de volume fini pour la mesure de Busemann. On en déduit que si Ω n’est pas un triangle alors Ω est strictement convexe, à bord 𝒞 1 et qu’une surface projective convexe S est de volume fini si et seulement si la surface duale est de volume fini.

DOI : https://doi.org/10.5802/aif.2707
Classification:  57M50,  52C20,  22E40
Keywords: Surface, Hilbert’s geometry, Hyperbolic geometry, Lattice, Discrete subgroup of Lie group
@article{AIF_2012__62_1_325_0,
     author = {Marquis, Ludovic},
     title = {Surface Projective Convexe de volume fini},
     journal = {Annales de l'Institut Fourier},
     publisher = {Association des Annales de l'institut Fourier},
     volume = {62},
     number = {1},
     year = {2012},
     pages = {325-392},
     doi = {10.5802/aif.2707},
     mrnumber = {2986273},
     zbl = {1254.57015},
     language = {fr},
     url = {http://www.numdam.org/item/AIF_2012__62_1_325_0}
}
Marquis, Ludovic . Surface Projective Convexe de volume fini. Annales de l'Institut Fourier, Volume 62 (2012) no. 1, pp. 325-392. doi : 10.5802/aif.2707. http://www.numdam.org/item/AIF_2012__62_1_325_0/

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