A fourth-order regularization of the curvature flow of immersed plane curves with Dirichlet boundary conditions

Giovanni Bellettini; Virginia Lorenzini; Matteo Novaga; Riccardo Scala

doi:10.48550/arxiv.2601.04385

A fourth-order regularization of the curvature flow of immersed plane curves with Dirichlet boundary conditions

arXiv (Cornell University) 2026 Preprint Open access

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Authors: Giovanni Bellettini, Virginia Lorenzini, Matteo Novaga, Riccardo Scala

DOI: 10.48550/arxiv.2601.04385

Cited by: 0

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.

Fields of Study & Subjects

Geometric Analysis and Curvature Flows Nonlinear Partial Differential Equations Geometry and complex manifolds

Publication details

Journal / source: arXiv (Cornell University)
Publication date: 7 January 2026
Document type: Preprint