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On the characterization of $p$-harmonic functions on the Heisenberg group by mean value properties

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  • We characterize $p-$harmonic functions in the Heisenberg group in terms of an asymptotic mean value property, where $1 < p <\infty$, following the scheme described in [16] for the Euclidean case. The new tool that allows us to consider the subelliptic case is a geometric lemma, Lemma 3.2 below, that relates the directions of the points of maxima and minima of a function on a small subelliptic ball with the unit horizontal gradient of that function.
    Mathematics Subject Classification: Primary: 35J60, 35R03; Secondary: 35J70.

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