Classification and Liouville type theorems for p-harmonic morphisms

We prove firstly the classification theorem for p- harmonic morphisms between Euclidean domains. Secondly, we show that if phi : M -> N is a p-harmonic morphism (p >= 2) from a complete Riemannian manifold M of nonnegative Ricci curvature into a Riemannian manifold N of non-positive scalar curvature such that the L-q-energy is finite, then f is constant, which improve the corresponding result due to G. Choi, G. Yun in (Geometriae Dedicata 101 ( 2003), 53-59).