A survey of the elastic flow of curves and networks

Abstract

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.

References in corpus (4)

• Convergence of elastic flows of curves into manifolds
• The Lojasiewicz-Simon inequality for the elastic flow
• Length-constrained curve diffusion
• Elastic flow of networks: short-time existence result

Cited by in corpus (8)

• Convergence of elastic flows of curves into manifolds
• Li-Yau type inequality for curves in any codimension
• General rigidity principles for stable and minimal elastic curves
• A dynamic approach to heterogeneous elastic wires
• Complete classification of planar p-elasticae
• The $p$-elastic flow for planar closed curves with constant parametrization
• On p-biharmonic curves
• On an elastic flow for parametrized curves in ${\mathbb{R}}^n$ suitable for numerical purposes