Mattia Fogagnolo, Andrea Pinamonti
Published 2020-11-09Version 1
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.
Comments: Accepted for publication in "Mathematics in Engineering"
On the $C^{1,α}$ Regularity of $p$-Harmonic Functions in the Heisenberg Group
Convergence of Natural $p$-Means for the $p$-Laplacian in the Heisenberg Group
Isoperimetric inequalities and regularity of $A$-harmonic functions on surfaces
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