Cheng, XinyueShen, Zhongmin2024-02-012024-02-012022-02-07Cheng, 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/s00025-022-01605-8https://hdl.handle.net/1805/38284We 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.en-USAttribution 4.0 InternationalFinsler metricRicci curvatureweighted Ricci curvaturegeodesic ballvolume comparisonPoincar´e-Lichnerowicz inequalityArticle