摘要
We obtain the Laplacian comparison theorem and the Bishop- Gromov comparison theorem on a Finsler manifold with the weighted Ricci curvature Ric∞ bounded below. As applications, we prove that if the weighted Ricci curvature Ri∞ is bounded below by a positive number, then the manifold must have finite fundamental group, and must be compact if the distortion is also bounded. Moreover, we give the Calabi-Yau linear volume growth theorem on a Finsler manifold with nonnegative weighted Ricci curvature.
We obtain the Laplacian comparison theorem and the Bishop- Gromov comparison theorem on a Finsler manifold with the weighted Ricci curvature Ric∞ bounded below. As applications, we prove that if the weighted Ricci curvature Ri∞ is bounded below by a positive number, then the manifold must have finite fundamental group, and must be compact if the distortion is also bounded. Moreover, we give the Calabi-Yau linear volume growth theorem on a Finsler manifold with nonnegative weighted Ricci curvature.
基金
This work was supported in part by the Natural Science Foundation of Anhui Province （No. 1608085MA03） and the National Natural Science Foundation of China （Grant No. 11471246）.
