%0 Journal Article
%T From Funk to Hilbert Geometry
%A Athanase Papadopoulos
%A Marc Troyanov
%J Mathematics
%D 2014
%I arXiv
%X We survey some basic geometric properties of the Funk metric of a convex set in $\mathbb{R}^n$. In particular, we study its geodesics, its topology, its metric balls, its convexity properties, its perpendicularity theory and its isometries. The Hilbert metric is a symmetrization of the Funk metric, and we show some properties of the Hilbert metric that follow directly from the properties we prove for the Funk metric.
%U http://arxiv.org/abs/1406.6983v1