Construction of Triply Periodic Minimal Surfaces

2010/02/25 by Rami Younes, Younes, Rami
Materials Science · Mathematics · #53A10 #Differential Geometry (math.DG) #FOS: Mathematics #Geometric and Algebraic Topology #Mathematical Dynamics and Fractals #Quasicrystal Structures and Properties

paper · pdf · doi:10.48550/arxiv.1002.4805

openalex publication_date 2010/02/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Given a tiling 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 T×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.

Citations

• The Geometries of 3-Manifolds

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