Abstract : Let $M$ be a complete Riemannian manifold and let $N$ be a Riemannian manifold of non-positive sectional curvature. Assume that $Ric^M \geq-{4(p-1)\over p^2}\mu_0$ at all $x\in M$ and ${\rm Vol}(M)$ is infinite, where $\mu_0>0$ is the infimum of the spectrum of the Laplacian acting on $L^2$-functions on $M$. Then any $p$-harmonic map $\phi:M\to N$ of finite $p$-energy is constant. Also, we study Liouville type theorem for $p$-harmonic morphism.

Keywords : $p$-harmonic map, $p$-harmonic morphism, Liouville type theorem