A Compact Non-convex Ancient Curve Shortening Flow

TL;DR

This paper constructs a compact, non-convex ancient solution to the curve shortening flow that asymptotically resembles the Yin-Yang curve, expanding understanding of ancient solutions in geometric flows.

Contribution

It introduces a novel example of a compact, non-convex ancient solution for the curve shortening flow, which was previously unknown.

Findings

Provides the first known example of a non-convex ancient solution

Shows the solution is asymptotic to the Yin-Yang curve

Advances understanding of ancient solutions in geometric flows

Abstract

An example of a compact, non-convex, embedded ancient solution for the curve shortening flow, which is asymptotic to Yin-Yang curve, is constructed.