One thousand and one higher-order geometric flows of networks

Luca Benatti; Alessandra Pluda

One thousand and one higher-order geometric flows of networks

Analysis of PDEs 2026-07-15 v1

Authors: Luca Benatti , Alessandra Pluda

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.

Keywords

geometric flows higher-order functionals curvature networks short-time existence long-time existence

Cite

@article{arxiv.2607.13894,
  title  = {One thousand and one higher-order geometric flows of networks},
  author = {Luca Benatti and Alessandra Pluda},
  journal= {arXiv preprint arXiv:2607.13894},
  year   = {2026}
}

Comments

47 pages, comments are welcome!