Embedded triply periodic zero mean curvature surfaces of mixed type in Lorentz-Minkowski 3-space

TL;DR

This paper constructs embedded triply periodic zero mean curvature surfaces of mixed type in Lorentz-Minkowski 3-space, sharing the same topology as the classical Schwarz D surface in Euclidean space.

Contribution

It introduces a novel class of zero mean curvature surfaces in Lorentz-Minkowski space with specific topological properties.

Findings

Constructed embedded triply periodic zero mean curvature surfaces

Surfaces have the same topology as Schwarz D surface

Demonstrated existence of such surfaces in Lorentz-Minkowski 3-space

Abstract

We construct embedded triply periodic zero mean curvature surfaces of mixed type in the Lorentz-Minkowski 3-space with the same topology as the Schwarz D surface in the Euclidean 3-space.