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arXiv:1002.4805 [math.DG]AbstractReferencesReviewsResources

Construction of Triply Periodic Minimal Surfaces

Rami Younes

Published 2010-02-25, updated 2010-03-12Version 3

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.

Comments: The paper has been removed so that it could be uploaded correctly!
Categories: math.DG
Subjects: 53A10
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