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arXiv · 1210.2881

On the Characterization of p-Harmonic Functions on the Heisenberg Group by Mean Value Properties

Fausto Ferrari·Qing Liu·Juan J. Manfredi
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Abstract

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.

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Fausto Ferrari, Qing Liu, Juan J. Manfredi. 2012-10-10. On the Characterization of p-Harmonic Functions on the Heisenberg Group by Mean Value Properties. https://arxiv.org/abs/1210.2881

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