%0 Journal Article
%T Weighted Ricci curvature in Riemann-Finsler geometry
%J AUT Journal of Mathematics and Computing
%I Amirkabir University of Technology
%Z 2783-2449
%A Shen, Zhongmin
%D 2021
%\ 09/01/2021
%V 2
%N 2
%P 117-136
%! Weighted Ricci curvature in Riemann-Finsler geometry
%K Ricci curvature
%K $S$-curvature
%K Mean curvature
%R 10.22060/ajmc.2021.20473.1067
%X 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.
%U https://ajmc.aut.ac.ir/article_4500_fc3d11fc673b4e9a44f3b4e11ecbea4e.pdf