Asymptotic Properties of Hilbert Geometry

• Published in: Журнал математической физики, анализа, геометрии
• Date: 2008
• Main Authors: Borisenko, A.A., Olin, E.A.
• Format: Article
• Language: English
• Published: Фізико-технічний інститут низьких температур ім. Б.І. Вєркіна НАН України 2008
• Online Access: https://nasplib.isofts.kiev.ua/handle/123456789/106510
• Journal Title: Digital Library of Periodicals of National Academy of Sciences of Ukraine
• Cite this: Asymptotic Properties of Hilbert Geometry / A.A. Borisenko, E.A. Olin // Журнал математической физики, анализа, геометрии. — 2008. — Т. 4, № 3. — С. 327-345. — Бібліогр.: 16 назв. — англ.

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...