Calculus of Variations and Geometric Measure Theory

C. Mantegazza - A. Pluda - M. Pozzetta

A Survey of the Elastic Flow of Curves and Networks

created by pluda on 28 Sep 2020
modified on 28 Mar 2023


Published Paper

Inserted: 28 sep 2020
Last Updated: 28 mar 2023

Journal: Milan J. Math.
Volume: 89
Number: 1
Pages: 59-121
Year: 2021
Doi: 10.1007/s00032-021-00327-w

ArXiv: 2009.12870 PDF


We collect and present in a unified way several results in recent years about the elastic flow of curves and networks, trying to draw the state of the art of the subject. In particular, we give a complete proof of global existence and smooth convergence to critical points of the solution of the elastic flow of closed curves in $\mathbb{R}^2$. In the last section of the paper we also discuss a list of open problems.