Asian Journal of Mathematics

Volume 20 (2016)

Number 4

Saddle towers in Heisenberg space

Pages: 629 – 644

DOI: http://dx.doi.org/10.4310/AJM.2016.v20.n4.a2

Author

Sébastien Cartier (Laboratoire d’Analyse et de Mathématiques Appliquées, Université Paris-Est, Créteil, France)

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 supported on domains is not bounded in Heisenberg space.

Keywords

Heisenberg space, minimal surfaces, saddle tower, Scherk surface, symmetric surfaces, deformation of surfaces, barrier construction, supported minimal surfaces

2010 Mathematics Subject Classification

53A10, 53C42

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