Asymptotic Properties of Hilbert Geometry

Details Asymptotic Properties of Hilbert Geometry Asymptotic Properties of Hilbert Geometry

2007-11-03

arxiv.org/abs/0711.0446v1

Journal of Mathematical Physics, Analysis, Geometry, vol 4, N 3, 2008, 327 - 345

Mathematics

Differential Geometry

18 pages, 2 figures. The paper is appeared to publish in "Journal of Mathematical Physic, Analys, Geometry" which is printed i

Scientific paper

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

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