MATEMATIČKI VESNIK
МАТЕМАТИЧКИ ВЕСНИК



MATEMATIČKI VESNIK
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.

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Keywords: Minimal submanifolds; $p$-harmonic function; Liouville type theorem.

MSC: 58E20, 53C42

Pages:  494$-$498     

Volume  65 ,  Issue  4 ,  2013