AbstractTriply 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 a...
Abstract:We prove two main theorems about equivariant minimal surfaces in an arbitrary nonpositively curved symmetric spaces extending classical results on minimal surfaces in Euclidean space. First, we show that a complete equivariant branched immersed minimal surface in a nonpositively curved symmetric space of finite total curvature must be of finite Morse index. It is a generalization of t...