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arXiv · 0711.1664

Some comparison theorems in Finsler-Hadamard manifolds

Alexandr A. Borisenko·Eugeny A. Olin
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Abstract

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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Alexandr A. Borisenko, Eugeny A. Olin. 2007-11-11. Some comparison theorems in Finsler-Hadamard manifolds. https://arxiv.org/abs/0711.1664

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