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arXiv · 1903.00795

Minimal surfaces with non-trivial topology in the three-dimensional Heisenberg group

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

We study symmetric minimal surfaces in the three-dimensional Heisenberg group $\mathrm{Nil}_3$ using the generalized Weierstrass type representation, the so-called loop group method. In particular, we will discuss how to construct minimal surfaces in $\mathrm{Nil}_3$ with non-trivial topology. Moreover, we will classify equivariant minimal surfaces given by one-parameter subgroups of the isometry group $\mathrm{Iso}_{\circ}(\mathrm{Nil}_3)$ of $\mathrm{Nil}_3$.

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Josef F. Dorfmeister, Jun-ichi Inoguchi, Shimpei Kobayashi. 2019-03-03. Minimal surfaces with non-trivial topology in the three-dimensional Heisenberg group. https://arxiv.org/abs/1903.00795

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