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 ${\mathbb{H}}^n$ with $n\ge 2$. The first one is an improvement of a result of Monti and is the natural reformulation in ${\mathbb{H}}^n$ of the classical Lipschitz approximation in ${\mathbb{R}}^n$. The second one is an adaptation of the approximation via maximal function developed by De Lellis and Spadaro.

25 pages

References in corpus (1)

• Smoothness of Lipschitz minimal intrinsic graphs in Heisenberg groups $H^n,n>1$

Cited by in corpus (2)

• Symmetric double bubbles in the Grushin plane
• Rickman rugs and intrinsic bilipschitz graphs