Improved Lipschitz approximation of H-perimeter minimizing boundaries

Abstract

We prove two new approximation results of H-perimeter minimizing boundaries by means of intrinsic Lipschitz functions in the setting of the Heisenberg group Hn with n≥2. The first one is an improvement of [19] and is the natural reformulation in Hn of the classical Lipschitz approximation in Rn. The second one is an adaptation of the approximation via maximal function developed by De Lellis and Spadaro [11].