weighted ricci curvature in riemann-finsler geometry

Ricci curvature is one of the important geometric quantities in riemann-finsler geometry. together with the s-curvature, one can define a weighted ricci curvature for a pair of finsler metric and a volume form on a manifold. one can build up a bridge from riemannian geometry to finsler geometry via geodesic fields. then one can estimate the laplacian of a distance function and the mean curvature of a metric sphere under a lower weighted ricci curvature by applying the results in the riemannian setting. these estimates also give rise to a volume comparison of bishop-gromov type for finsler metric measure manifolds.