Browsing by Subject "Poincar´e-Lichnerowicz inequality"

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    Some Inequalities on Finsler Manifolds with Weighted Ricci Curvature Bounded Below
    (Springer, 2022-02-07) Cheng, Xinyue; Shen, Zhongmin; Mathematical Sciences, School of Science
    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.