TY - JOUR
ID - 4500
TI - Weighted Ricci curvature in Riemann-Finsler geometry
JO - AUT Journal of Mathematics and Computing
JA - AJMC
LA - en
SN - 2783-2449
AU - Shen, Zhongmin
AD - Department of Mathematical Sciences, Indiana University-Purdue University, 402 N Blackford Street, Indianapolis, IN 46202,
USA
Y1 - 2021
PY - 2021
VL - 2
IS - 2
SP - 117
EP - 136
KW - Ricci curvature
KW - $S$-curvature
KW - Mean curvature
DO - 10.22060/ajmc.2021.20473.1067
N2 - 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.
UR - https://ajmc.aut.ac.ir/article_4500.html
L1 - https://ajmc.aut.ac.ir/article_4500_fc3d11fc673b4e9a44f3b4e11ecbea4e.pdf
ER -