Minimal surfaces and harmonic functions in the Heisenberg group

作者：Monti Roberto^*

来源：Nonlinear Analysis-Theory Methods & Applications, 2015, 126: 378-393.

DOI：10.1016/j.na.2015.03.013

• Heisenberg group
• Regularity of H-minimal surfaces
• H-harmonic functions

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

• 出版日期2015-10