Nonplanar ancient curve shortening flows in $\mathbb{R}^3$ from grim reapers

TL;DR

This paper constructs new nonplanar ancient solutions to the curve shortening flow in three-dimensional space by combining grim reapers in perpendicular planes, expanding understanding of eternal solutions in geometric flows.

Contribution

It introduces a novel method of creating nonplanar eternal solutions to the curve shortening flow using perpendicular grim reapers, which was not previously known.

Findings

Construction of nonplanar ancient solutions in $\

 in $\\mathbb{R}^3$

Solutions built from perpendicular grim reapers

Abstract

In this note we construct new nonplanar ancient (in fact, eternal) solutions to the curve shortening flow in $\mathbb{R}^3$, built out of translating grim reapers laying in perpendicular planes.