# Short time existence of the classical solution to the fractional Mean curvature flow

## TL;DR

This paper proves that smooth solutions to the fractional mean curvature flow exist for a short time when starting from bounded, regular initial sets, including volume-preserving cases.

## Contribution

It establishes the short-time existence of solutions for the fractional mean curvature flow and volume-preserving variants, extending the understanding of these geometric flows.

## Key findings

- Short-time existence of smooth solutions proven
- Results apply to volume-preserving fractional mean curvature flow
- Solutions exist for initial sets with C^{1,1} regularity

## Abstract

We establish short-time existence of the smooth solution to the fractional mean curvature flow when the initial set is bounded and C^{1,1}-regular. We provide the same result also for the volume preserving fractional mean curvature flow.