曲面射影凸体积有限
Surface projective convexe de volume fini
摘要：
凸射影曲面是$\mathbb{P}(\R)$的一个真凸开$Ω$与$\mathrm{SL}_3(\R)$的一个离散子群$Γ$的商。本文给出了凸射影曲面在Busemann测度下具有有限体积这一事实的一些特征。我们推导出，如果$Ω$不是一个三角形，那么$Ω$是严格凸的，有$\Cc^1$边界和凸射影曲面$S$是有限体积的当且仅当对偶曲面是有限体积的。
英文摘要：
A convex projective surface is the quotient of a properly convex open $Ω$ of $\mathbb{P}(\R)$ by a discret subgroup $Γ$ 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 $Ω$ is not a triangle then $Ω$ 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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
