Self-similar curve shortening flow in hyperbolic 2-space

TL;DR

This paper classifies all self-similar solutions of the curve shortening flow in hyperbolic 2-space, completing the understanding of such flows in all constant curvature 2D spaces.

Contribution

It provides a complete classification of self-similar solutions in hyperbolic space, extending previous classifications in Euclidean and spherical geometries.

Findings

Classification of self-similar solutions in hyperbolic space

Completes the classification in all 2D constant curvature spaces

Links with prior work on Euclidean and spherical cases

Abstract

We find and classify self-similar solutions of the curve shortening flow in standard hyperbolic 2-space. Together with earlier work of Halld\'orsson on curve shortening flow in the plane and Santos dos Reis and Tenenblat in the 2-sphere, this completes the classification of self-similar curve shortening flows in the constant curvature model spaces in 2-dimensions.