Liouville Type Theorem About p-Harmonic Function and p-Harmonic Map with Finite L-Energy

This paper deals with the $p$-harmonic function on a complete non-compact submanifold $M$ isometrically immersed in an $(n + k)$-dimensional complete Riemannian manifold $\ov{M}$ of non-negative $(n - 1)$-th Ricci curvature. The Liouville type theorem about the $p$-harmonic map with finite $L^{q}$-energy from complete submanifold in a partially non-negatively curved manifold to non-positively curved manifold is also obtained.