Comparison theorems on Finsler manifolds with weighted Ricci curvature bounded below

doi:10.1007/s11464-018-0692-1

Front. Math. China

2018, Vol. 13

Issue (2) : 435-448 https://doi.org/10.1007/s11464-018-0692-1

RESEARCH ARTICLE

Comparison theorems on Finsler manifolds with weighted Ricci curvature bounded below

Songting YIN(

)

Department of Mathematics and Computer Science, Tongling University, Tongling 244000, China

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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

Corresponding Author(s): Songting YIN

Issue Date: 28 March 2018

Cite this article:

Songting YIN. Comparison theorems on Finsler manifolds with weighted Ricci curvature bounded below[J]. Front. Math. China, 2018, 13(2): 435-448.

URL:

https://academic.hep.com.cn/fmc/EN/10.1007/s11464-018-0692-1
https://academic.hep.com.cn/fmc/EN/Y2018/V13/I2/435

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