arXiv:1707.09176 [math.DG]AbstractReferencesReviewsResources
Construction of embedded periodic surfaces in $\mathbb{R}^n$
Karsten Grosse-Brauckmann, Susanne Kürsten
Published 2017-07-28Version 1
We construct embedded minimal surfaces which are $n$-periodic in $\mathbb{R}^n$. They are new for codimension $n-2\ge 2$. We start with a Jordan curve of edges of the $n$-dimensional cube. It bounds a Plateau minimal disk which Schwarz reflection extends to a complete minimal surface. Studying the group of Schwarz reflections, we can characterize those Jordan curves for which the complete surface is embedded. For example, for $n=4$ exactly five such Jordan curves generate embedded surfaces. Our results apply to surface classes other than minimal as well, for instance polygonal surfaces.
Comments: 27 pages, 5 figures
Categories: math.DG
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