Preprint

Inserted: 24 jul 2025
Last Updated: 24 jul 2025

Year: 2025
Links: ArXiv

Abstract:

Using a geometric construction, we solve Plateau's Problem in the Heisenberg group $\mathbb{H}^1$ for intrinsic graphs defined on a convex domain $D$, under a smallness condition either on the boundary $\partial D$ or on the Lipschitz boundary datum $\phi : \partial D \to \mathbb{R}$. The proof relies on a calibration argument. We then apply these techniques to establish a new regularity result for $H$-perimeter minimizers.