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arXiv · 2602.20865

High Codimension Curve Shortening Flow with Free Boundary

Huy The Nguyen·Artemis A. Vogiatzi
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Abstract

We study curve shortening flow in high codimension for arcs with free boundary meeting a fixed smooth barrier orthogonally. We prove dilation-invariant curvature and higher-derivative estimates up to the boundary using a Stahl-type localised maximum principle and an adapted cut-off. Using a reflected Gaussian entropy and blow-up analysis, Type I boundary singularities yield a shrinking semicircle model after reflection. Type II blow-ups give a Grim Reaper translator, which is ruled out under a free-boundary entropy bound $<2$. Hence in the low-entropy regime the flow either converges to the orthogonal chord or has only semicircle boundary singularities.

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Huy The Nguyen, Artemis A. Vogiatzi. 2026-02-24. High Codimension Curve Shortening Flow with Free Boundary. https://arxiv.org/abs/2602.20865

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