\(\newcommand{\R}{\mathbb{R}} \newcommand{\HH}{\mathbb{H}} \newcommand{\Z}{\mathbb{Z}} \newcommand{\K}{\mathbb{K}} \newcommand{\N}{\mathbb{N}} \newcommand{\cV}{\mathcal{V}}\)

The Bernstein problem for ruled graphs in the Heisenberg group

For best results, please download the models and open them in Preview, Paint 3D, or any other 3D modeling program.

Figure 1: A broken plane. A ruled surface made of two half-planes and two wedges.

Figure 2: A conjectural area-minimizing competitor for the broken plane.

Figure 3: A conjectural energy-minimizing competitor for the broken plane.