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

Yingbo Han; Shuxiang Feng

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

Authors

Yingbo Han College of Mathematics and Information Science, Xinyang Normal University, Xinyang, 464000, Henan, P. R. China Author
Shuxiang Feng College of Mathematics and Information Science, Xinyang Normal University, Xinyang, 464000, Henan, P. R. China Author

Keywords:

Minimal submanifolds, $p$-harmonic function, Liouville type theorem

Subjects:

58E20, 53C42

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.

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Published

2013-10-15

Issue

Vol. 65 No. 4 (2013): Vol. 65, Issue 4

Section

Articles

License

This work is licensed under a Creative Commons Attribution 4.0 International License.