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

摘要

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