Evolution of closed curves by length-constrained curve diffusion

DOI10.1090/proc/14473zbMath1433.53117arXiv1901.07128OpenAlexW3099838323MaRDI QIDQ5223180

Glen Wheeler, Yuhan Wu, James A. McCoy

Publication date: 17 July 2019

Published in: Proceedings of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1901.07128

zbMATH Keywords

curvature flowcurve diffusion flowdifferential geometry of plane curveshigher-order quasilinear partial differential equation

Mathematics Subject Classification ID

Heat and other parabolic equation methods for PDEs on manifolds (58J35) Flows related to mean curvature (53E10)

Related Items (3)

A sixth order flow of plane curves with boundary conditions ⋮ A survey of the elastic flow of curves and networks ⋮ Short time existence for higher order curvature flows with and without boundary conditions

Cites Work

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• The polyharmonic heat flow of closed plane curves
• On the curve diffusion flow of closed plane curves
• Finite time singularities for the locally constrained Willmore flow of surfaces
• Lifespan theorem for constrained surface diffusion flows
• Convergence in gradient-like systems with applications to PDE
• The shrinking figure eight and other solitons for the curve diffusion flow
• Mixed volume preserving curvature flows
• Evolution of Elastic Curves in $\Rn$: Existence and Computation
• Global analysis of the generalised Helfrich flow of closed curves immersed in ℝⁿ

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