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Surface Projective Convexe de volume fini
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Une surface projective convexe est le quotient d’un ouvert proprement convexe Ω de l’espace projectif réel ℙ 2 (ℝ) par un sous-groupe discret Γ de SL 3 (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 ???? 1 et qu’une surface projective convexe S est de volume fini si et seulement si la surface duale est de volume fini.
Title: Surface Projective Convexe de volume fini
Description:
Une surface projective convexe est le quotient d’un ouvert proprement convexe Ω de l’espace projectif réel ℙ 2 (ℝ) par un sous-groupe discret Γ de SL 3 (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 ???? 1 et qu’une surface projective convexe S est de volume fini si et seulement si la surface duale est de volume fini.
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