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Infinite Periodic Discrete Minimal Surfaces Without Self-Intersections

Wayne Rossman
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Abstract

A triangulated piecewise-linear minimal surface in Euclidean 3-space defined using a variational characterization is critical for area amongst all continuous piecewise-linear variations with compact support that preserve the simplicial structure. We explicitly construct examples of such surfaces that are embedded and are periodic in three independent directions of Euclidean 3-space.

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Wayne Rossman. 2004-10-13. Infinite Periodic Discrete Minimal Surfaces Without Self-Intersections. https://arxiv.org/abs/math/0410314

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