Some Inequalities on Finsler Manifolds with Weighted Ricci Curvature Bounded Below

dc.contributor.authorCheng, Xinyue
dc.contributor.authorShen, Zhongmin
dc.contributor.departmentMathematical Sciences, School of Science
dc.date.accessioned2024-02-01T21:32:05Z
dc.date.available2024-02-01T21:32:05Z
dc.date.issued2022-02-07
dc.description.abstractWe 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.versionFinal published version
dc.identifier.citationCheng, 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.urihttps://hdl.handle.net/1805/38284
dc.language.isoen_US
dc.publisherSpringer
dc.relation.isversionof10.1007/s00025-022-01605-8
dc.relation.journalResults in Mathematics
dc.rightsAttribution 4.0 Internationalen
dc.rights.urihttp://creativecommons.org/licenses/by/4.0/
dc.sourceArXiv
dc.subjectFinsler metric
dc.subjectRicci curvature
dc.subjectweighted Ricci curvature
dc.subjectgeodesic ball
dc.subjectvolume comparison
dc.subjectPoincar´e-Lichnerowicz inequality
dc.titleSome Inequalities on Finsler Manifolds with Weighted Ricci Curvature Bounded Below
dc.typeArticle
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