Asymptotic Foliations of Quasi-Homogeneous Convex Affine Domains

Abstract

Abstract. In this paper, we prove that the automorphism group of a quasi-homogeneous properly convex affine domain in R n acts transitively on the set of all the extreme points of the domain. This set is equal to the set of all the asymptotic cone points coming from the asymptotic foliation of the domain and thus it is a homogeneous submanifold of R n .