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<p>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.</p>

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

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2026年4月24日

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  • Anna Dall’Acqua,
  • Manuel Schlierf

摘要

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.