### Mathematics in Engineering

2021, Issue 6: 1-15. doi: 10.3934/mine.2021046
Research article Special Issues

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

• Received: 03 July 2020 Accepted: 06 November 2020 Published: 13 November 2020
• 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.

Citation: Mattia Fogagnolo, Andrea Pinamonti. Strict starshapedness of solutions to the horizontal p-Laplacian in the Heisenberg group[J]. Mathematics in Engineering, 2021, 3(6): 1-15. doi: 10.3934/mine.2021046

### Related Papers:

• 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.

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