Triply Periodic Minimal Surfaces of genus 3

Abstract

Triply Periodic Minimal Surfaces (TPMSs) are minimal surfaces in flat 3-tori. I will review recently discovered examples of genus 3, with explicit or implicit Weierstrass data. They are all inspired by physics and material sciences. Minimal surfaces of other types have also been constructed as side products. The techniques may construct more TPMSs of genus 3, which we were numerically aware, and plan to rigorously prove in the near future.