Evolving convex curves by a generalized length-preserving flow

TL;DR

This paper introduces a generalized flow that preserves length for convex curves in the plane, demonstrating that it exists globally and transforms any convex curve into a circle over time.

Contribution

It presents a new generalized length-preserving flow and proves its global existence and convergence to circles for convex curves.

Findings

Flow exists globally for convex curves

Convex curves deform into circles over time

Flow preserves length during evolution

Abstract

This paper deals with a generalized length-preserving flow for convex curves in the plane. It is shown that the flow exists globally and deforms convex curves into circles as time tends to infinity.