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

Abstract

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 discuss how to construct minimal surfaces in Nil 3 with non-trivial topology. Moreover, we will classify equivariant minimal surfaces given by oneparameter subgroups of the isometry group Iso • (Nil 3 ) of Nil 3 .