Classification and Liouville type theorems for p-harmonic morphisms

Abstract

We prove firstly the classification theorem for p-harmonic morphisms between Euclidean domains. Secondly, we show that if \(\phi: M\to N\) 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 Lq-energy is finite, then \(\phi\) is constant, which improve the corresponding result due to G. Choi, G. Yun in (Geometriae Dedicata 101 (2003), 53–59).