Triply Periodic Minimal Surfaces Bounded by Vertical Symmetry Planes

TL;DR

This paper presents a unified, elementary approach to constructing many classical and new triply periodic minimal surfaces in Euclidean space, utilizing a Schwarz-Christoffel formula for periodic polygons, emphasizing their symmetry properties.

Contribution

It introduces a novel, simplified method for generating triply periodic minimal surfaces using Schwarz-Christoffel formulas, highlighting their vertical symmetry plane features.

Findings

Unified construction method for classical and new triply periodic minimal surfaces

Surfaces are cut into simply connected pieces by vertical symmetry planes

Provides explicit formulas for periodic polygons

Abstract

We give a uniform and elementary treatment of many classical and new triply periodic minimal surfaces in Euclidean space, based on a Schwarz-Christoffel formula for periodic polygons in the plane. Our surfaces share the property that vertical symmetry planes cut them into simply connected pieces.