Local gradient estimate for harmonic functions on Finsler manifolds
Calculus of variations and partial dierential equations
Mathematics - Analysis of PDEs | Mathematics - Differential Geometry
arxiv: Mathematics::Differential Geometry | Mathematics::Metric Geometry | Mathematics::Symplectic Geometry
In this paper, we prove the local gradient estimate for harmonic functions on complete, noncompact Finsler measure spaces under the condition that the weighted Ricci curvature has a lower bound. As applications, we obtain Liouville type theorem on Finsler manifolds with nonnegative Ricci curvature.