Some Liouville-type theorems for harmonic functions on Finsler manifolds

In this paper, we give some Liouville-type theorems for L p ( p ∈ R ) harmonic (resp. subharmonic, superharmonic) functions on forward complete Finsler manifolds. Moreover, we derive a gradient estimate for harmonic functions on a closed Finsler manifold. As an application, one obtains that any harmonic function on a closed Finsler manifold with nonnegative weighted Ricci curvature Ric N ( N ∈ ( n , ∞ ) ) must be constant.