# Convex ancient solutions to curve shortening flow

## TL;DR

This paper classifies all convex ancient solutions to the curve shortening flow, showing they are limited to a specific set of known solutions, thus completing a significant classification effort.

## Contribution

It completes the classification of convex ancient solutions to the curve shortening flow, identifying all possible solutions.

## Key findings

- Only stationary lines, shrinking circles, Grim Reapers, and Angenent ovals are convex ancient solutions.
- The classification confirms no other convex ancient solutions exist.
- The result completes the classification initiated by previous researchers.

## Abstract

We show that the only convex ancient solutions to curve shortening flow are the stationary lines, shrinking circles, Grim Reapers and Angenent ovals, completing the classification initiated by Daskalopoulos, Hamilton and Sesum and X.-J. Wang