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arXiv · 2207.13414

The prescribed mean curvature equation for $t$-graphs in the sub-Finsler Heisenberg group $\mathbb{H}^n$

Gianmarco Giovannardi·Andrea Pinamonti·Julián Pozuelo·Simone Verzellesi
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Abstract

We study the sub-Finsler prescribed mean curvature equation, associated to a strictly convex body $K_0 \subseteq \mathbb{R}^{2n}$, for $t$-graphs on a bounded domain $\Omega$ in the Heisenberg group $\mathbb{H}^n$. When the prescribed datum $H$ is constant and strictly smaller that the Finsler mean curvature of $\partial \Omega$, we prove the existence of a Lipschitz solution to the Dirichlet problem for the sub-Finsler CMC equation by means of a Finsler approximation scheme.

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Gianmarco Giovannardi, Andrea Pinamonti, Julián Pozuelo, Simone Verzellesi. 2022-07-27. The prescribed mean curvature equation for $t$-graphs in the sub-Finsler Heisenberg group $\mathbb{H}^n$. https://arxiv.org/abs/2207.13414

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