Asymptotic Properties of Hilbert Geometry - Borisenko, A. A.; Olin, E. A. (Журнал математичної фізики, аналізу, геометрії, 2008)
It is shown that the spheres in Hilbert geometry have the same volume growth entropy as those in the Lobachevsky space. Asymptotic estimates for the ratio of the volume of metric ball to the area of the metric sphere in Hilbert geometry are given. Derived estimates agree with the well-known fact in the Lobachevsky space. Mathematics Subject Classification: 53C60, 58B20, 52A20.