Связь между объемом и площадью для шаров в многообразиях Финслера–Адамара

Abstract

We give upper and lower estimates for the ratio between the volume of a metric ball and the area of its surface in Finsler–Hadamard manifolds with pinched S-curvature. We apply these estimates to get the limit at infinity for this ratio. The derived estimates are a generalization of the well-known result in the Riemannian geometry.