For every order m≥2 and every admissible set of junction/endpoint conditions, the L²-gradient flow of ∫|∂s^m γ|²/2 + length/2 exists uniquely up to reparametrization for a short time, and either runs forever or degenerates in a controlled way.
A sixth order curvature flow of plane curves with boundary conditions
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One thousand and one higher-order geometric flows of networks
For every order m≥2 and every admissible set of junction/endpoint conditions, the L²-gradient flow of ∫|∂s^m γ|²/2 + length/2 exists uniquely up to reparametrization for a short time, and either runs forever or degenerates in a controlled way.