Amirkabir University of TechnologyAUT Journal of Mathematics and Computing2783-24492220210901Weighted Ricci curvature in Riemann-Finsler geometry117136450010.22060/ajmc.2021.20473.1067ENZhongminShenDepartment of Mathematical Sciences, Indiana University-Purdue University, 402 N Blackford Street, Indianapolis, IN 46202,
USA0000-0001-8074-3944Journal Article20210826Ricci 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.https://ajmc.aut.ac.ir/article_4500_fc3d11fc673b4e9a44f3b4e11ecbea4e.pdf