Asymptotic Properties of Hilbert Geometry
arXiv:0711.0446
Abstract
We show that the spheres in Hilbert geometry have the same volume growth entropy as those in the Lobachevsky space. We give the asymptotic estimates for the ratio of the volume of metric ball to the area of the metric sphere in Hilbert geometry. Derived estimates agree with the well-known fact in the Lobachevsky space
18 pages, 2 figures. The paper is appeared to publish in "Journal of Mathematical Physic, Analys, Geometry" which is printed in Ukraine