Asymptotic Properties of Hilbert Geometry
Alexander A. Borisenko, Eugeny A. Olin
TL;DR
This paper investigates the asymptotic volume growth properties of Hilbert geometry, demonstrating that its spheres exhibit entropy similar to Lobachevsky space and providing estimates for volume-to-area ratios.
Contribution
It establishes the asymptotic volume growth entropy of Hilbert geometry spheres and compares it with Lobachevsky space, offering new geometric estimates.
Findings
Hilbert geometry spheres have the same volume growth entropy as Lobachevsky space.
Asymptotic estimates for volume-to-sphere area ratios in Hilbert geometry.
Results align with known properties of Lobachevsky space.
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
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Taxonomy
TopicsGeometric Analysis and Curvature Flows · Point processes and geometric inequalities · Geometry and complex manifolds