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

Harmonic graphs in the Heisenberg group

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Figure 1: Examples of \(H\)-minimal and contact harmonic graphs with singularities. In both cases, the surfaces consist of horizontal line segments which intersect only along the characteristic nexus.

Figure 2: An \(H\)-minimal graph with branched characteristic nexus.

Figure 3: An energy-minimizing graph based on the middle-thirds Cantor set.