论文标题
改善Bochner不平等的一些重要应用在Finsler歧管上
Some important applications of improved Bochner inequality on Finsler manifolds
论文作者
论文摘要
我们在加权的RICCI曲率$ \ mathrm {ric} _ {\ infty} \ geq k $中，通过使用改进的bochner不平等及其集成形式来建立一些重要的不等式。首先，我们获得了尖锐的庞加莱 - 荷奈洛维奇不平等。此外，我们为对数Sobolev不等式提供了新的证明。最后，我们获得了测量球体积的估计。
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.
