Self-similar solutions to the mean curvature flow in the Minkowski plane $\mathbf R^{1,1}$

TL;DR

This paper studies the mean curvature flow of curves in the Minkowski plane, classifies all self-similar solutions, and presents five additional exact solutions, expanding understanding of geometric flows in pseudo-Euclidean spaces.

Contribution

It introduces the mean curvature flow in Minkowski space and provides a complete classification of self-similar solutions along with five explicit solutions.

Findings

Classification of all self-similar solutions in Minkowski plane

Identification of five additional exact solutions

Enhanced understanding of geometric flows in pseudo-Euclidean geometry

Abstract

We introduce the mean curvature flow of curves in the Minkowski plane $\mathbf R^{1,1}$ and give a classification of all the self-similar solutions. In addition, we describe five other exact solutions to the flow.