A Toponogov-Type Comparison Theorem for Finsler Manifolds and its Applications

In this paper, we introduce the notion of modified flag curvature for Finsler metrics which naturally come from Hessian comparison theorem. We then establish a Toponogov-type comparison theorem for Finsler manifolds with nonnegative-modified flag curvature. As its applications, we prove that the fundamental group of any forward complete Finsler manifold (M, F) with nonnegative-modified flag curvature is finitely generated; furthermore, if additional M has bounded Cartan tensor, then M is of finite topological type.