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PreprintCC BY 4.0arXiv

The Bonnet-Myers theorem on Finsler manifolds with integral weighted Ricci curvature bounds

  • Xinyue Cheng
  • Liulin Liu
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Abstract

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.

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Cite

BibTeXRIS
BibTeX
@misc{cheng2026bonnetmyers,
  title = {{The Bonnet-Myers theorem on Finsler manifolds with integral weighted Ricci curvature bounds}},
  author = {Xinyue Cheng and Liulin Liu},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.02686},
  eprint = {2609.02686},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.02686},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - The Bonnet-Myers theorem on Finsler manifolds with integral weighted Ricci curvature bounds
AU  - Xinyue Cheng
AU  - Liulin Liu
PY  - 2026
DA  - 2026/09/02
PB  - arXiv
DO  - 10.48550/arxiv.2609.02686
UR  - https://arxiv.org/abs/2609.02686
AB  - 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.
ER  -