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arXiv · 1210.7300

A loop group method for minimal surfaces in the three-dimensional Heisenberg group

Josef F. Dorfmeister·Jun-ichi Inoguchi·Shimpei Kobayashi
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Abstract

We characterize constant mean curvature surfaces in the three-dimensional Heisenberg group by a family of flat connections on the trivial bundle $\D \times \GL$ over a simply connected domain $\mathbb{D}$ in the complex plane. In particular for minimal surfaces, we give an immersion formula, the so-called Sym-formula, and a generalized Weierstrass type representation via the loop group method.

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Josef F. Dorfmeister, Jun-ichi Inoguchi, Shimpei Kobayashi. 2012-10-27. A loop group method for minimal surfaces in the three-dimensional Heisenberg group. https://arxiv.org/abs/1210.7300

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