Some comparison theorems in Finsler-Hadamard manifolds
Differential Geometry
2011-10-11 v1 Complex Variables
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.
Cite
@article{arxiv.0711.1664,
title = {Some comparison theorems in Finsler-Hadamard manifolds},
author = {Alexandr A. Borisenko and Eugeny A. Olin},
journal= {arXiv preprint arXiv:0711.1664},
year = {2011}
}
Comments
15 pages