  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 Manfredi et al. (2009) 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.
