Gradient Estimate and Liouville Theorems for p-Harmonic Maps

In this paper, we first obtain an L q gradient estimate for p -harmonic maps, by assuming the target manifold supporting a certain function, whose gradient and Hessian satisfy some analysis conditions. From this L q gradient estimate, we get a corresponding Liouville type result for p -harmonic maps. Secondly, using these general results, we give various geometric applications to p -harmonic maps from complete manifolds with nonnegative Ricci curvature to manifolds with various upper bound on sectional curvature, under appropriate controlled images.