UPPER BOUNDS ON THE DIAMETER FOR FINSLER MANIFOLDS WITH WEIGHTED RICCI CURVATURE.

In this paper we obtain some Cheeger-Gromov-Taylor type compactness theorems for a forward complete and connected Finsler manifold of dimensional n ≥ 2 via weighted Ricci curvatures. The proofs are based on the index form of a minimal unit speed geodesic segment, Bochner-Weitzenböck formula and Hessian comparison theorem. [ABSTRACT FROM AUTHOR]