Regularity of Lipschitz boundaries with prescribed sub-Finsler mean curvature in the Heisenberg group ${\mathbb{H}}^1$

Gianmarco Giovannardi, Manuel Ritoré

For a strictly convex set $K\subset {\mathbb{R}}^2$ of class $C^2$ we consider its associated sub-Finsler $K$-perimeter $|\partial E{|}_K$ in ${\mathbb{H}}^1$ and the prescribed mean cur…