Zhurnal Matematicheskoi Fiziki, Analiza, Geometrii [Journal of Mathematical Physics, Analysis, Geometry]
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Zhurnal Matematicheskoi Fiziki, Analiza, Geometrii [Journal of Mathematical Physics, Analysis, Geometry], 2008, Volume 4, Number 3, Pages 327–345 (Mi jmag100)  
This article is cited in 2 scientific papers (total in 2 papers)

Asymptotic properties of Hilbert geometry

A. A. Borisenko, E. A. Olin

Department of Mechanics and Mathematics, V.N. Karazin Kharkiv National University 4 Svobody Sq., Kharkiv, 61077, Ukraine
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Abstract: 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.
Key words and phrases: Hilbert geometry, Finsler geometry, balls, spheres, volume, area, entropy.
Received: 02.11.2007
Bibliographic databases:
Document Type: Article
MSC: 53C60, 58B20, 52A20
Language: English
Citation: A. A. Borisenko, E. A. Olin, “Asymptotic properties of Hilbert geometry”, Zh. Mat. Fiz. Anal. Geom., 4:3 (2008), 327–345
Citation in format AMSBIB
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\by A.~A.~Borisenko, E.~A.~Olin
\paper Asymptotic properties of Hilbert geometry
\jour Zh. Mat. Fiz. Anal. Geom.
\yr 2008
\vol 4
\issue 3
\pages 327--345
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\zmath{https://zbmath.org/?q=an:1167.53066}
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    • This publication is cited in the following 2 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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