Liouville type theorem about p-harmonic function and p-harmonic map with finite L q -energy

Abstract

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 $$\overline M $$ 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.