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

We study symmetric minimal surfaces in the three-dimensional Heisenberg group Nil(3) using the generalized Weierstrass type representation, the so-called loop group method. In particular, we will present a general scheme for how to construct minimal surfaces in Nil(3) with non-trivial geometry. Special emphasis will be put on equivariant minimal surfaces. Moreover, we will classify equivariant minimal surfaces given by one-parameter subgroups of the isometry group Iso(degrees)(Nil(3)) of Nil(3).