{"paper":{"title":"Surface projective convexe de volume fini","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GT","authors_text":"Ludovic Marquis","submitted_at":"2009-02-18T13:54:14Z","abstract_excerpt":"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."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0902.3143","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}