| A Liouville type theorem for $p$-harmonic functions on minimal submanifolds in $\Bbb R^{n+m}$ |
| Yingbo Han and Shuxiang Feng |
Abstract 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 $|du|^{2p-2}\in L^1(M)$, then $u$ is constant.
|
Keywords: Minimal submanifolds; $p$-harmonic function; Liouville type theorem. |
MSC: 58E20, 53C42 |
Pages: 494--498 |
Volume 65 , Issue 4 , 2013 |
