# On the rate of convergence of the $p$-curve shortening flow

## TL;DR

This paper establishes improved and likely sharp rates of convergence for the p-curve shortening flow when p is an integer greater than or equal to 1, advancing understanding of the flow's behavior.

## Contribution

It provides new, sharper convergence rate estimates for the p-curve shortening flow, enhancing previous results and likely representing the optimal rates.

## Key findings

- Improved convergence rate estimates for p-curve shortening flow.
- Results are probably sharp, indicating optimality.
- Advances understanding of flow dynamics for p ≥ 1.

## Abstract

In this paper we give rates of convergence for the $p$-curve shortening flow for $p\geq 1$ an integer, which improves on the known estimates and which are probably sharp.