# Uniqueness of regular shrinkers with 2 closed regions

## TL;DR

This paper proves the uniqueness of a specific regular shrinker, called the Cisgeminate eye, with two closed regions in planar network curvature flow, and explores some degenerate cases.

## Contribution

It establishes the uniqueness of the regular shrinker with two closed regions and identifies the Cisgeminate eye as this unique shape.

## Key findings

- Uniqueness of the Cisgeminate eye as the regular shrinker with 2 closed regions
- Existence of some degenerate regular shrinkers with 2 closed regions
- Application of Huisken's monotonicity formula to classify shrinkers

## Abstract

Regular shrinkers describe blow-up limits of a finite-time singularity of the motion by curvature of planar network of curves. This follows from Huisken's monotonicity formula. In this paper, we show that there is only one regular shrinker with 2 closed regions. This regular shrinker is the Cisgeminate eye. Moreover, we find some degenerate regular shrinkers with 2 closed regions.