no. 1
Surface Projective Convexe de volume fini
Marquis, Ludovic 1
1 tabacckludge ’Ecole Normale Supérieure de Lyon Unité de Mathématiques Pures et Appliquées 46, allée d’Italie 69364 Lyon Cedex 07 (France)
Annales de l'Institut Fourier, Tome 62 (2012) no. 1, pp. 325-392.

Une surface projective convexe est le quotient d’un ouvert proprement convexe Ω de l’espace projectif réel ℙ2(ℝ) par un sous-groupe discret Γ de SL3(ℝ). 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 𝒞1 et qu’une surface projective convexe S est de volume fini si et seulement si la surface duale est de volume fini.

A convex projective surface is the quotient of a properly convex open Ω of the projective real space ℙ2(ℝ) by a discrete subgroup Γ of SL3(ℝ). 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 𝒞1 boundary and that a convex projective surface S is of finite volume if and only if the dual surface is of finite volume.

DOI : 10.5802/aif.2707
Classification : 57M50, 52C20, 22E40
Mots-clés : surface, géométrie de Hilbert, géométrie hyperbolique, réseau, sous-groupes discrets des groupes de Lie
Keywords: Surface, Hilbert’s geometry, Hyperbolic geometry, Lattice, Discrete subgroup of Lie group

Marquis, Ludovic  1

1 tabacckludge ’Ecole Normale Supérieure de Lyon Unité de Mathématiques Pures et Appliquées 46, allée d’Italie 69364 Lyon Cedex 07 (France) 
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Marquis, Ludovic . Surface Projective Convexe de volume fini. Annales de l'Institut Fourier, Tome 62 (2012) no. 1, pp. 325-392. doi : 10.5802/aif.2707. https://aif.centre-mersenne.org/articles/10.5802/aif.2707/

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