Liouville type theorems for p-harmonic maps

LetM be a complete Riemannian manifold and let N be a Riemannian manifold of non-positive sectional curvature. Assume that RicM −4(p−1) p2 μ0 at all x ∈M and > −4(p−1) p2 μ0 at some point x0 ∈M, where μ0 > 0 is the least eigenvalue of the Laplacian acting on L2-functions on M. Let 2 q p. Then any q-harmonic map φ :M →N of finite q-energy is constant. Moreover, if N is a Riemannian manifold of non-positive scalar curvature, then any q-harmonic morphism φ :M →N of finite q-energy is constant. © 2007 Elsevier Inc. All rights reserved