Strict starshapedness of solutions to the horizontal p-laplacian in the Heisenberg group

We examine the geometry of the level sets of particular horizontally $p$-harmonic functions in the Heisenberg group. We find sharp, natural geometric conditions ensuring that the level sets of the $p$-capacitary potential of a bounded annulus in the Heisenberg group are strictly starshaped.
Comment: Accepted for publication in "Mathematics in Engineering"