Hilbert geometry for strictly convex domains - Colbois, Bruno; Verovic, Patrick (My University, 2004)
We prove in this paper that the Hilbert geometry associated with a bounded open convex domain C in R-n whose boundary partial derivativeC is a C-2 hypersuface with nonvanishing Gaussian curvature is bi-Lipschitz equivalent to the n-dimensional hyperbolic space H-n. Moreover, we show that the balls in such a Hilbert geometry have the same volume growth entropy as those in H-n.
Keywords: convex sets; Finsler spaces; metric geometry