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On the volume mean value property for $M$-Harmonic functions

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Abstract

We will show that if $U$ is a Bergman ball $E(a;\delta)$ in $B_n \subset \mathbb C^n$ and if $U$ has $M$--harmonic volume mean value property at $a$ for all $M$--harmonic functions $f$ on $\overline U$, then $U$ must be a ball centered at the origin with $a=0$.

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