Finite volume convex projective surface (Q442129)

This paper studies convex projective surfaces, i.e.~quotients of properly convex open subsets \(\Omega\) of the real projective plane by discrete subgroups of \(\mathrm{SL}_3(\mathbb{R})\). While much classical work is concerned with cocompact groups, the focus of the paper under review is on groups of finite covolume (with respect to the Busemann measure.)NEWLINENEWLINESeveral characterizations of the finite volume condition are given. As a consequence, it is proved that if \(\Omega\) is not a triangle, then it is strictly convex and has \(\mathcal{C}^1\) boundary. Another result is that a convex projective surface has finite volume if and only if its dual surface has finite volume.