A Liouville type theorem for $p$-harmonic functions on minimal submanifolds in $\Bbb R^{n+m}$
Keywords:
Minimal submanifolds, $p$-harmonic function, Liouville type theoremSubjects:
58E20, 53C42Abstract
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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2013-10-15
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