Minimal cylinders in the three-dimensional Heisenberg group

2022/06/14 by Kobayashi, Shimpei
#58E20 #Differential Geometry (math.DG) #FOS: Mathematics #Primary 53A10 #Secondary 53C42

paper · doi:10.48550/arxiv.2206.06625

Abstract

We study minimal cylinders in the three-dimensional Heisenberg group \rm Nil₃ using the generalized Weierstrass type representation, the so-called loop group method. We characterize all non-vertical minimal cylinders in terms of pairs of two closed plane curves which have the same signed area. Moreover, as a byproduct of the construction, spacelike CMC cylinders can also be obtained.

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• A solution to the Bernstein problem in the three-dimensional Heisenberg group via loop groups