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arXiv · 2607.13894

One thousand and one higher-order geometric flows of networks

Luca Benatti·Alessandra Pluda
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Abstract

We show short-time existence and uniqueness up to reparametrization for a large class of higher-order geometric flows of curves and networks obtained as $L^2$-gradient flow of higher-order functionals involving derivatives of the curvature. Additionally, we prove a long-time existence result via energy methods.

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Luca Benatti, Alessandra Pluda. 2026-07-15. One thousand and one higher-order geometric flows of networks. https://arxiv.org/abs/2607.13894

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