Journal of the
Korean Mathematical Society JKMS

We establish some Hessian comparison theorems and volume comparison theorems for Riemann-Finsler manifolds under various line radial integral curvature bounds. As their applications, we obtain some results on first eigenvalue, Gromov pre-compactness and generalized Myers theorem for Riemann-Finsler manifolds under suitable line radial integral curvature bounds. Our results are new even in the Riemannian case.

Keywords: extreme volume form, Finsler manifold, Gromov pre-compact\-ness, first eigenvalue, diameter

MSC numbers: Primary 53C60; Secondary 53B40