Accepted Paper

Inserted: 27 jul 2022
Last Updated: 26 jun 2024

Journal: Adv. Math.
Year: 2024

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.

Keywords: Heisenberg group, prescribed mean curvature, Constant Mean Curvature, Sub-Finsler Structure

Download:

• preprint