Frontiers of Mathematics in China

, Volume 13, Issue 2, pp 435–448

# Comparison theorems on Finsler manifolds with weighted Ricci curvature bounded below

Research Article

## Abstract

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 Ric 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.

## Keywords

Finsler manifold distortion S-curvature weighted Ricci curvature comparison theorem

53C60 53B40

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## Notes

### Acknowledgements

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).

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© Higher Education Press and Springer-Verlag GmbH Germany, part of Springer Nature 2018

## Authors and Affiliations

1. 1.Department of Mathematics and Computer ScienceTongling UniversityTonglingChina