Blow-ups of minimal surfaces in the Heisenberg group

Abstract

In this paper, we revise Monti's results on the blow-ups of H-perimeter minimizing sets in ${\mathbb{H}}^n$. 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 $n\ge 2$. However, the partial differential equation he derived for this limit function $\ddot{I}†$ through contact variation is incorrect. Instead, the correct equation is that the horizontal Laplacian of the limit function $\ddot{I}†$ is independent of the coordinate $y_1$ and solves equation 1 weakly.