Title: Integral curvatures of Finsler manifolds and applications,
Abstract: In this paper, we study the integral curvatures of Finsler manifolds. Some
Bishop-Gromov relative volume comparisons and several Myers type theorems are
obtained. We also establish a Gromov type precompactness theorem and a
Yamaguchi type finiteness theorem. Furthermore, the isoperimetric and Sobolev
constants of a closed Finsler manifold are estimated by integral curvature
bounds.