Some comparison theorems in Finsler-Hadamard manifolds

Details Some comparison theorems in Finsler-Hadamard manifolds Some comparison theorems in Finsler-Hadamard manifolds

2007-11-11

arxiv.org/abs/0711.1664v1

Journal of Math. Phys., Anal., Geometry. vol 3, N 3, 2007, pp. 298 - 312

Mathematics

Differential Geometry

15 pages

Scientific paper

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

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