@article {
author = {Shen, Zhongmin},
title = {Weighted Ricci curvature in Riemann-Finsler geometry},
journal = {AUT Journal of Mathematics and Computing},
volume = {2},
number = {2},
pages = {117-136},
year = {2021},
publisher = {Amirkabir University of Technology},
issn = {2783-2449},
eissn = {2783-2287},
doi = {10.22060/ajmc.2021.20473.1067},
abstract = {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.},
keywords = {Ricci curvature,$S$-curvature,Mean curvature},
url = {https://ajmc.aut.ac.ir/article_4500.html},
eprint = {https://ajmc.aut.ac.ir/article_4500_ea40c5a079b5b80106a3dd83e1b985fa.pdf}
}