On a curvature flow model for embryonic epidermal wound healing

TL;DR

This paper investigates a curvature flow model for embryonic epidermal wound healing, demonstrating that convex curves shrink to round points and analyzing the singularity profile and blowup classification.

Contribution

It introduces a curvature flow model specific to wound healing and provides new results on the shape evolution and singularity behavior of curves under this flow.

Findings

Convex curves shrink to round points in finite time.

The singularity profile after rescaling is circular.

Provides maximal time estimates for the flow.

Abstract

The paper studies a curvature flow linked to the physical phenomenon of wound closure. Under the flow we show that a closed, initially convex or close-to-convex curve shrinks to a round point in finite time. We also study the singularity, showing that the singularity profile after continuous rescaling is that of a circle. We additionally give a maximal time estimate, with an application to the classification of blowups.