Blow-ups of minimal surfaces in the Heisenberg group

Abstract

In this article, we revise Monti’s results on blow-ups of H-perimeter minimizing sets in Hn{{\mathbb{H}}}^{n}. Monti demonstrated that the Lipschitz approximation of the blow-up, after rescaling by the square root of the excess, converges to a limit function for n≥2n\ge 2. However, the partial differential equation he derived for this limit function φ\varphi through contact variation is incorrect. Instead, the limit function solves the following equation weakly∂∂y1Δ0φ=0,\frac{\partial }{\partial {y}_{1}}{\Delta }_{0}\varphi =0,

Keywords

• minimal surfaces
• heisenberg group
• intrinsic lipschitz graph
• 040a30