Abstract

In this article, we prove various properties and some Liouville type theorems for quasi-strongly p-harmonic maps. We also describe conditions that quasi-strongly p-harmonic maps become p-harmonic maps. We prove that if <TEX>$\phi$</TEX> : <TEX>$M\;\longrightarrow\;N$</TEX> is a quasi-strongly p-harmonic map (\rho\; <TEX>$\geq\;2$</TEX>) from a complete noncompact Riemannian manifold M of nonnegative Ricci curvature into a Riemannian manifold N of non-positive sectional curvature such that the <TEx>$(2\rho－2)$</TEX>-energy, <TEX>$E_{2p-2}(\phi)$</TEX> is finite, then <TEX>$\phi$</TEX> is constant.