Saddle towers in Heisenberg space

TL;DR

This paper constructs highly symmetric periodic minimal surfaces called Saddle towers in Heisenberg space, using barriers to ensure convergence, revealing unbounded numbers of disjoint minimal graphs.

Contribution

It introduces a novel barrier construction method for minimal surfaces in Heisenberg space, enabling the creation of symmetric Saddle towers and demonstrating unbounded disjoint minimal graphs.

Findings

Constructed symmetric Saddle towers in Heisenberg space.

Developed a barrier method for minimal surface convergence.

Showed the number of disjoint minimal graphs is unbounded.

Abstract

We construct most symmetric Saddle towers in Heisenberg space i.e. periodic minimal surfaces that can be seen as the desingularization of vertical planes intersecting equiangularly. The key point is the construction of a suitable barrier to ensure the convergence of a family of bounded minimal disks. Such a barrier is actually a periodic deformation of a minimal plane with prescribed asymptotic behavior. A consequence of the barrier construction is that the number of disjoint minimal graphs suppoerted on domains is not bounded in Heisenberg space.