Geodesic
Asymptotic properties of Hilbert geometry
Žurnal matematičeskoj fiziki, analiza, geometrii, Tome 4 (2008) no. 3, pp. 327-345 
A. A. Borisenko; E. A. Olin. Asymptotic properties of Hilbert geometry. Žurnal matematičeskoj fiziki, analiza, geometrii, Tome 4 (2008) no. 3, pp. 327-345. http://geodesic.mathdoc.fr/item/JMAG_2008_4_3_a0/
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Voir la notice de l'article provenant de la source Math-Net.Ru

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.

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