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Demonstrates global existence and subconvergence to critical points in hypersurface flows, implying stability in curves with free boundaries.
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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Dall’Acqua et al. (2026) studied this question.
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