AI 中文总结
该研究在芬斯勒度量测度流形上，推导了受积分加权里奇曲率控制的体积比较定理，建立非同心球的Bishop-Gromov体积比较定理，进而证明了具积分加权里奇曲率界的芬斯勒流形上的博内-迈尔斯型定理。
AI 中文摘要
本文中，我们在芬斯勒度量测度流形上推导了一些新的相对体积比较定理和Bishop-Gromov体积比较定理，所有这些都由积分加权里奇曲率控制。特别地，我们建立了非同心球的Bishop-Gromov体积比较定理，在此基础上，证明了具积分加权里奇曲率界的芬斯勒度量测度流形上的博内-迈尔斯型定理。
英文摘要
In this paper, we derive some new relative volume comparison theorems and Bishop-Gromov volume comparisons on Finsler metric measure manifolds, all of which are controlled by the integral weighted Ricci curvature. In particular, we establish a Bishop-Gromov volume comparison theorem for nonconcentric balls. Based on these, we prove a theorem of Bonnet-Myers type on Finsler metric measure manifolds with integral weighted Ricci curvature bounds.
Comments32 pages. Any comments and suggestions are warmly welcome
