A Liouville type theorem for $p$-harmonic functions on minimal submanifolds in $\Bbb R^{n+m}$

Yingbo Han, Shuxiang Feng

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