# Minimal surfaces and harmonic functions in the Heisenberg group

created by monti on 20 Mar 2015

[BibTeX]

Accepted Paper

Inserted: 20 mar 2015
Last Updated: 20 mar 2015

Journal: Nonlinear Analysis Series A: Theory, Methods & Applications
Year: 2015

Abstract:

We study the blow-up of $H$-perimeter minimizing sets in the Heisenberg group $\mathbb H^n$, $n\geq 2$. We show that the Lipschitz approximations rescaled by the square root of excess converge to a limit function. Assuming a stronger notion of local minimality, we prove that this limit function is harmonic for the Kohn Laplacian in a lower dimensional Heisenberg group.