Some important applications of improved Bochner inequality on Finsler manifolds

Abstract

We establish some important inequalities under the condition that the weighted Ricci curvature ${\mathrm{Ric}}_{\infty }\ge K$ 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.

14 pages

References in corpus (1)

• Some fundamental problems in global Finsler geometry