The prescribed mean curvature equation for t-graphs in the sub-Finsler Heisenberg group Hn

We study the sub-Finsler prescribed mean curvature equation, associated to a strictly convex body K0 subset of R2n, for t -graphs on a bounded domain Omega in the Heisenberg group Hn. When the prescribed datum H is constant and strictly smaller than the Finsler mean curvature of partial derivative 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. (c) 2024 The Author(s). Published by Elsevier Inc. This is an open access article under the CC BY -NC -ND license (http://creativecommons .org /licenses /by -nc -nd /4 .0/).