Dynamics of Elastic Wires: Preserving Area without Nonlocality

Abstract

We derive an $H^{-1}$-gradient flow of the elastic energy which preserves the enclosed area of evolving planar curves. For this new sixth-order evolution equation, we prove a global existence result. Additionally, by penalizing the length, we show convergence to an area constrained critical point of the elastic energy.

arXiv comment32 pages, 2 figures. Final version. Comments are welcome!

References in corpus (7)

• Cylindrical equilibrium shapes of fluid membranes
• The Łojasiewicz-Simon gradient inequality for open elastic curves
• The Lojasiewicz-Simon inequality for the elastic flow
• On the Lojasiewicz-Simon gradient inequality on submanifolds
• Closed ideal planar curves
• Optimal thresholds for preserving embeddedness of elastic flows
• Existence and convergence of the length-preserving elastic flow of clamped curves

Cited by in corpus (1)

• A new energy method for shortening and straightening complete curves