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arXiv · 1002.4805

Construction of Triply Periodic Minimal Surfaces

Rami Younes
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Abstract

Given a tiling $\mathcal{T}$ of the plane by straight edge polygons, which is invariant by two independent translations, we construct a family of embedded triply periodic minimal surfaces which desingularizes $\mathcal{T}\times\mathbb{R}$. For this purpose, inspired by the work of Martin Traizet, we open the nodes of singular Riemann surfaces to glue together simply periodic Karcher saddle towers, each placed at a vertex of the tiling in such a way that its wings go along the corresponding edges of the tiling ending at that vertex.

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Rami Younes. 2010-03-12. Construction of Triply Periodic Minimal Surfaces. https://arxiv.org/abs/1002.4805

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