A distance comparison principle for curve flows with a global forcing term

TL;DR

This paper extends the distance comparison principle to closed plane curves evolving under a global forcing term, providing new insights into their geometric behavior and curvature constraints.

Contribution

It introduces a novel distance comparison principle for curve flows with global forcing, applicable to curves with specific curvature bounds.

Findings

Established a Huisken-like distance comparison principle for curves with global forcing

Demonstrated the principle applies to curves with local total curvature above -pi

Provided theoretical framework for analyzing curve evolution with forcing terms

Abstract

We consider closed, embedded, smooth curves in the plane and study their behaviour under curve flows with a global forcing term. We prove an analogue to Huisken's distance comparison principle for curve shortening flow for initial curves whose local total curvature does not lie below -pi and arbitrary global forcing terms.