Some volume comparison theorems on Finsler manifolds of weighted Ricci curvature bounded below

This paper mainly studies the volume comparison in Finsler geometry under the condition that the weighted Ricci curvature Ric∞ has a lower bound. By using the Laplacian comparison theorems of distance function, we characterize the growth ratio of the volume coefficients. Further, some volume comparison theorems of Bishop-Gromov type are obtained.

Keywords:

volume comparison , the weighted Ricci curvature , Laplacian comparison theorem , distance function , volume coefficient