On the Hilbert Geometry of Convex Polytopes

Abstract

We survey the Hilbert geometry of convex polytopes. In particular we present two important characterisations of these geometries, the first one in terms of the volume growth of their metric balls, the second one as a bi-lipschitz class of the simplexe's geometry.

To appear in the Handbook on Hilbert geometry edited by G. Besson, A. Papadopoulos and M. Troyanov

References in corpus (2)

• On the Hilbert Geometry of Convex Polytopes
• Hilbert domains quasi-isometric to normed vector spaces

Cited by in corpus (1)

• On the Hilbert Geometry of Convex Polytopes