A Liouville type theorem for p-harmonic functions on minimal submanifolds in Rn+m

Abstract

In this note, we prove that if an $n$-dimensionalcomplete noncompact minimal submanifold $M$ in $R^{n+m}$ hassufficiently small total scalar curvature, and $u$ is a$p$-harmonic function on $M$ with $|du{|}^{2p-2}ın{L}^1(M)$, then$u$ is constant.