Lipschitz Characterisation of Polytopal Hilbert Geometries

Abstract

We prove that the Hilbert Geometry of a convex set is bi-lipschitz equivalent to a normed vector space if and only if the convex is a polytope.

Extends our previous result with B. Colbois and P. Verovic arXiv:0804.1620v1. Main Theorem independently and differently proved by Andreas Bernig

References in corpus (4)

• Hilbert geometry for convex polygonal domains
• Spectral Radius and Amenability in Hilbert Geometries
• Hilbert domains quasi-isometric to normed vector spaces
• Hilbert geometry of polytopes

Cited by in corpus (1)

• On the Hilbert Geometry of Convex Polytopes