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

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 ${\mathrm{Nil}}_3$.

59 pages, the version 2 has been changed substantially

References in corpus (1)

• Minimal translation surfaces in the Heisenberg group Nil3