On rough-isometry classes of Hilbert geometries

Thomas Foertsch

Vol. 245 (2010), No. 2, 227–238

DOI: 10.2140/pjm.2010.245.227

Abstract

We prove that Hilbert geometries on uniformly convex Euclidean domains with C²-boundaries are roughly isometric to the real hyperbolic spaces of corresponding dimension.

Keywords

Hilbert geometries, Gromov hyperbolicity, rough isometry

Mathematical Subject Classification 2000

Primary: 53C60

Secondary: 51F99

Milestones

Received: 30 July 2009

Accepted: 1 October 2009

Published: 1 April 2010