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arXiv · 2009.02632

Some important applications of improved Bochner inequality on Finsler manifolds

Xinyue Cheng
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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 Poincaré-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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Xinyue Cheng. 2020-09-06. Some important applications of improved Bochner inequality on Finsler manifolds. https://arxiv.org/abs/2009.02632

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