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2020•Mathematics in EngineeringOpen access

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

Mattia Fogagnolo, 1 Centro di Ricerca Matematica Ennio De Giorgi, Scuola Normale Superiore, Piazza dei Cavalieri 3, 56126 Pisa (PI), Italy, Andrea Pinamonti, 2 Universita degli Studi di Trento, via Sommarive 14, 38123 Povo (TN), Italy, <sup>†</sup><b>This contribution is part of the Special Issue:</b> Partial Differential Equations from theory to applications—Dedicated to Alberto Farina, on the occasion of his 50th birthday, Guest Editors: Serena Dipierro; Luca Lombardini, Link: <a href="www.aimspress.com/mine/article/5752/special-articles" target="_blank">www.aimspress.com/mine/article/5752/special-articles</a>

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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.

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What this paper is about

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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Available 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.

Key concepts: Heisenberg group, Annulus (botany), Bounded function, Group (periodic table), Laplace operator, Mathematics, Pure mathematics, Harmonic function

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