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

Abstract

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.

Keywords

• p-laplacian
• p-harmonic
• stashaped level sets
• heisenberg group