# Stacking disorder in periodic minimal surfaces

## TL;DR

This paper constructs non-periodic minimal surfaces with stacking disorder in a 3D space, inspired by crystallography and experimental observations of defects, revealing new insights into the structure of minimal surfaces.

## Contribution

It introduces a novel family of non-periodic minimal surfaces in a product space, modeling stacking disorder and twinning defects observed experimentally.

## Key findings

- Constructed 1-parameter families of non-periodic minimal surfaces.
- Surfaces converge to foliations by tori in the product space.
- Reproduces experimental twinning defects as stacking disorder cases.

## Abstract

We construct 1-parameter families of non-periodic embedded minimal surfaces of infinite genus in $T \times \mathbb{R}$, where $T$ denotes a flat 2-tori. Each of our families converges to a foliation of $T \times \mathbb{R}$ by $T$. These surfaces then lift to minimal surfaces in $\mathbb{R}^3$ that are periodic in horizontal directions but not periodic in the vertical direction. In the language of crystallography, our construction can be interpreted as disordered stacking of layers of periodically arranged catenoid necks. Our work is motivated by experimental observations of twinning defects in periodic minimal surfaces, which we reproduce as special cases of stacking disorder.