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arXiv · 2503.13219

The length-preserving elastic flow with free boundary on hypersurfaces in $\mathbb{R}^n$

Anna Dall'Acqua·Manuel Schlierf
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Abstract

We study the length-preserving elastic flow of curves in arbitrary codimension with free boundary on hypersurfaces. This constrained gradient flow is given by a nonlocal evolution equation with nonlinear higher-order boundary conditions. We prove global existence and subconvergence to critical points. The proof strategy involves a careful treatment of short-time existence, uniqueness, and parabolic energy estimates.

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Anna Dall'Acqua, Manuel Schlierf. 2025-03-17. The length-preserving elastic flow with free boundary on hypersurfaces in $\mathbb{R}^n$. https://arxiv.org/abs/2503.13219

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