# Triply periodic zero mean curvature surfaces in Lorentz-Minkowski 3-space

## TL;DR

This paper constructs triply periodic zero mean curvature surfaces of mixed type in Lorentz-Minkowski 3-space, mirroring the topology of Euclidean minimal surfaces like Schwarz rPD surfaces, expanding understanding of such geometries.

## Contribution

It introduces new triply periodic zero mean curvature surfaces in Lorentz-Minkowski space with topology similar to Euclidean minimal surfaces, a novel extension in differential geometry.

## Key findings

- Constructed triply periodic zero mean curvature surfaces in Lorentz-Minkowski space.
- Surfaces share topology with Schwarz rPD minimal surfaces.
- Demonstrated existence of such surfaces of mixed type.

## Abstract

We construct triply periodic zero mean curvature surfaces of mixed type in the Lorentz-Minkowski 3-space, with the same topology as the triply periodic minimal surfaces in the Euclidean 3-space, called Schwarz rPD surfaces.