Some Inequalities on Finsler Manifolds with Weighted Ricci Curvature Bounded Below
dc.contributor.author | Cheng, Xinyue | |
dc.contributor.author | Shen, Zhongmin | |
dc.contributor.department | Mathematical Sciences, School of Science | |
dc.date.accessioned | 2024-02-01T21:32:05Z | |
dc.date.available | 2024-02-01T21:32:05Z | |
dc.date.issued | 2022-02-07 | |
dc.description.abstract | We establish some important inequalities under a lower weighted Ricci curvature bound on Finsler manifolds. Firstly, we establish a relative volume comparison of Bishop–Gromov type. As one of the applications, we obtain an upper bound for volumes of the Finsler manifolds. Further, when the S-curvature is bounded on the whole manifold, we obtain a theorem of Bonnet–Myers type on Finsler manifolds. Finally, we obtain a sharp Poincaré–Lichnerowicz inequality by using integrated Bochner inequality, from which we obtain a better lower bound for the first eigenvalue on the Finsler manifolds. | |
dc.eprint.version | Final published version | |
dc.identifier.citation | Cheng, X., & Shen, Z. (2022). Some Inequalities on Finsler Manifolds with Weighted Ricci Curvature Bounded Below. Results in Mathematics, 77(2), 70. https://doi.org/10.1007/s00025-022-01605-8 | |
dc.identifier.uri | https://hdl.handle.net/1805/38284 | |
dc.language.iso | en_US | |
dc.publisher | Springer | |
dc.relation.isversionof | 10.1007/s00025-022-01605-8 | |
dc.relation.journal | Results in Mathematics | |
dc.rights | Attribution 4.0 International | en |
dc.rights.uri | http://creativecommons.org/licenses/by/4.0/ | |
dc.source | ArXiv | |
dc.subject | Finsler metric | |
dc.subject | Ricci curvature | |
dc.subject | weighted Ricci curvature | |
dc.subject | geodesic ball | |
dc.subject | volume comparison | |
dc.subject | Poincar´e-Lichnerowicz inequality | |
dc.title | Some Inequalities on Finsler Manifolds with Weighted Ricci Curvature Bounded Below | |
dc.type | Article |