Submitted Paper

Inserted: 7 jan 2026
Last Updated: 13 jan 2026

Year: 2026

Abstract:

We consider a fourth-order regularization of the curvature flow for an immersed plane curve with fixed boundary, using an elastica-type functional depending on a small positive parameter $\varepsilon$. We show that the approximating flow smoothly converges, as $\varepsilon \to 0^+$, to the curvature flow of the curve with Dirichlet boundary conditions for all times before the first singularity of the limit flow.

Keywords: higher order regularization, Curvature flow of immersed curves