# Symmetric self-shrinkers for the fractional mean curvature flow

## TL;DR

This paper demonstrates the existence of symmetric, shrinking solutions to the fractional mean curvature flow with multiple concentric spheres, highlighting their stability properties.

## Contribution

It introduces new symmetric solutions for the fractional mean curvature flow and analyzes their stability, expanding understanding of the flow's dynamics.

## Key findings

- Existence of homothetically shrinking solutions with concentric spheres.
- All solutions except the ball are dynamically unstable.
- Provides insights into the stability of symmetric solutions.

## Abstract

We show existence of homothetically shrinking solutions of the fractional mean curvature flow, whose boundary consists in a prescribed numbers of concentric spheres. We prove that all these solutions, except from the ball, are dynamically unstable.