On a length preserving curve flow

TL;DR

This paper introduces a novel length-preserving flow for convex plane curves, demonstrating global existence, increasing enclosed area, and convergence to a circle in smooth topology over time.

Contribution

It presents a new curve flow that preserves length and proves convergence to a circle, expanding understanding of geometric evolution processes.

Findings

Global existence of the flow

Monotonic increase of enclosed area

Convergence to a circle in C-infinity topology

Abstract

In this paper, we consider a new length preserving curve flow for convex curves in the plane. We show that the global flow exists, the area of the region bounded by the evolving curve is increasing, and the evolving curve converges to the circle in C-infinity topology as t goes to infinity.