Topology of complete Finsler manifolds with radial flag curvature   bounded below
  We recently established a Toponogov type triangle comparison theorem for a certain class of Finsler manifolds whose radial flag curvatures are bounded below by that of a von Mangoldt surface of revolution (arXiv:1205.3913). In this article, as its applications, we prove the finiteness of topological type and a diffeomorphism theorem to Euclidean spaces. 
Kei Kondo, Shin-ichi Ohta, Minoru Tanaka
math.DG