A Theorem of Liouville Type for p-Harmonic Morphisms

摘要

In this article we prove a Liouville type theorem for p-harmonic morphisms. We show that if Φ: M→Nis a p-harmonic morphism (p≥2) from a complete noncompact Riemannian manifold Mof nonnegative Ricci curvature into a Riemannian manifold Nof nonpositive scalar curvature such that the p-energy E p (Φ), or (2p−2)-energy E 2p−2(Φ) is finite, then Φ is constant.