A non-local area preserving curve flow

TL;DR

This paper introduces a non-local, area-preserving curve flow for convex planar curves, demonstrating global existence, non-increasing length, and convergence to a circle in smooth topology over time.

Contribution

It establishes the global existence and convergence properties of a novel non-local, area-preserving flow for convex curves.

Findings

Flow exists globally for convex curves.

Curve length decreases over time.

Curves converge to a circle smoothly.

Abstract

In this paper, we consider a kind of area preserving non-local flow for convex curves in the plane. We show that the flow exists globally, the length of evolving curve is non-increasing, and the curve converges to a circle in C^{\infty} sense as time goes into infinity.