Gromov pre-compactness theorems for nonreversible Finsler manifolds

In this paper, we consider general metric spaces and length spaces whose metrics may be nonreversible, and give Gromov pre-compactness theorems for such spaces with finite reversibility with respect to a generalized Gromov–Hausdorff distance. On the basis of these we derive pre-compactness theorems for general Finsler manifolds with finite reversibility.