Harmonic maps of finite energy for Finsler manifolds

In this paper, we study some properties of harmonic maps for Finsler manifolds. Some Liouville theorems on harmonic maps for Finsler manifolds are given. Let M be a complete simply connected Riemannian manifold with non-negative Ricci curvature and M¯ be a complete Berwald manifold with non-positive flag curvature. The main purpose of this paper is to prove that there exists no non-degenerate harmonic map ϕ from M to M¯ with ∫SMe(ϕ)dVSM<∞, which generalizes the result of Schoen and Yau (1976) from Riemannian manifolds to Berwald manifolds.