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Some important applications of improved Bochner inequality on Finsler manifolds (2009.02632v1)
Published 6 Sep 2020 in math.DG
Abstract: We establish some important inequalities under the condition that the weighted Ricci curvature $\mathrm{Ric}_{\infty}\geq K$ for some constant $K >0$ by using improved Bochner inequality and its integrated form. Firstly, we obtain a sharp Poincar\'{e}-Lichnerowicz inequality. Further, we give a new proof for logarithmic Sobolev inequality. Finally, we obtain an estimate of the volume of geodesic balls.
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