Some Comparison Theorems in Finsler-Hadamard Manifolds

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

Анотація

We give upper and lower bounds for the ratio of the volume of metric ball to the area of metric sphere in Finsler-Hadamard manifolds with the pinched S-curvature. We apply these estimates to find the limit at infinity for this ratio. The estimates derived are the generalization of the result well known in Riemannian geometry. We also estimate the volume growth entropy for the balls in these manifolds.

Mathematics Subject Classification: 53C60, 53C20.

Ключові слова:

Finsler geometry, Finsler-Hadamard manifolds, comparison theorems, balls, volume and area, entropy.

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Як цитувати

(1)
Borisenko, A. A.; Olin, E. A. Some Comparison Theorems in Finsler-Hadamard Manifolds. Журн. мат. фіз. анал. геом. 2007, 3, 298-312.

Номер

Том 3 № 3 (2007)

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