Regularity of Lipschitz boundaries with prescribed sub-Finsler mean curvature in the Heisenberg group H^1

For a strictly convex set K subset of R-2 of class C-2 we consider its associated sub-Finsler K-perimeter vertical bar partial derivative E vertical bar(K) in H-1 and the prescribed mean curvature functional vertical bar partial derivative E vertical bar(K) - integral(E) f associated to a continuous function f . Given a critical set for this functional with Euclidean Lipschitz and intrinsic regular boundary, we prove that their characteristic curves are of class C-2 and that this regularity is optimal. The result holds in particular when the boundary of E is of class C-1. (C) 2021 The Authors. Published by Elsevier Inc.