Minimal surfaces and harmonic functions in the Heisenberg group

Abstract

We study the blow-up of H-perimeter minimizing sets in the Heisenberg group Hn, n≥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.