Asymptotic Properties of Hilbert Geometry

Автор(и)

  • A.A. Borisenko Department of Mechanics and Mathematics, V.N. Karazin Kharkiv National University 4 Svobody Sq., Kharkiv, 61077, Ukraine
  • E.A. Olin Department of Mechanics and Mathematics, V.N. Karazin Kharkiv National University 4 Svobody Sq., Kharkiv, 61077, Ukraine

Ключові слова:

Hilbert geometry, Finsler geometry, balls, spheres, volume, area, entropy.

Анотація

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.

Mathematics Subject Classification: 53C60, 58B20, 52A20.

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Як цитувати

(1)
Borisenko, A.; Olin, E. Asymptotic Properties of Hilbert Geometry. Журн. мат. фіз. анал. геом. 2008, 4, 327-345.

Номер

Том 4 № 3 (2008)

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