Calculus of Variations and Geometric Measure Theory

R. Monti - G. Stefani

Improved Lipschitz Approximation of $H$-perimeter minimizing boundaries

created by monti on 28 Nov 2016
modified by stefani on 03 Oct 2021


Published Paper

Inserted: 28 nov 2016
Last Updated: 3 oct 2021

Journal: J. Math. Pures Appl.
Volume: 108
Number: 3
Pages: 372--398
Year: 2017
Doi: 10.1016/j.matpur.2017.04.002

ArXiv: 1612.00263 PDF


We prove two new approximation results of H-perimeter minimizing boundaries by means of intrinsic Lipschitz functions in the setting of the Heisenberg group $H^n$ with $n\ge2$. The first one is an improvement of $[19]$ and is the natural reformulation in $H^n$ of the classical Lipschitz approximation in $R^n$. The second one is an adaptation of the approximation via maximal function developed by De Lellis and Spadaro $[11]$.

Keywords: Heisenberg group, Regularity of $H$-minimal surfaces, Lipschitz approximation