Local gradient estimate for harmonic functions on Finsler manifolds (Q471106)

The study of harmonic functions is one of the central topics in geometric analysis, and in the Riemannian setting, a lot of interesting and important results have been obtained. The main goal of this paper is to generalize the local gradient estimate to Finsler manifolds. The author presents a local gradient estimate for harmonic functions on complete, noncompact Finsler measure spaces under the condition that the weighted Ricci curvature has a lower bound. This estimate is applied to obtain some Liouville-type theorems on noncompact Finsler manifolds with nonnegative Ricci curvature.