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curve networks 1geometric flows 1gradient flow 1higher-order PDE 1long-time existence 1

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math.AP2026

One thousand and one higher-order geometric flows of networks

Luca Benatti, Alessandra Pluda

The paper proves short-time existence and uniqueness (up to reparametrization) for many higher-order geometric flows of curves and networks derived as L²‑gradient flows of curvatur…