Global analysis of the generalised Helfrich flow of closed curves immersed in ℝⁿ

DOI10.1090/S0002-9947-2014-06592-6zbMath1321.53085arXiv1205.5939OpenAlexW1760422929MaRDI QIDQ5496662

Glen Wheeler

Publication date: 2 February 2015

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

Full work available at URL: https://arxiv.org/abs/1205.5939

zbMATH Keywords

\(L^2\)-gradient flowHelfrich flowclosed elastic curves

Mathematics Subject Classification ID

Optimization of shapes other than minimal surfaces (49Q10) Heat and other parabolic equation methods for PDEs on manifolds (58J35)

Related Items (12)

Noether's theorem and the Willmore functional ⋮ Geometric aspects of shape optimization ⋮ A dynamic approach to heterogeneous elastic wires ⋮ A gradient flow for the \(p\)-elastic energy defined on closed planar curves ⋮ The \(p\)-elastic flow for planar closed curves with constant parametrization ⋮ A dynamical approach to the variational inequality on modified elastic graphs ⋮ A sixth order flow of plane curves with boundary conditions ⋮ On a curvature flow model for embryonic epidermal wound healing ⋮ A survey of the elastic flow of curves and networks ⋮ Long time existence of solutions to an elastic flow of networks ⋮ A Second Order Gradient Flow of p-Elastic Planar Networks ⋮ Evolution of closed curves by length-constrained curve diffusion

Cites Work

• On the curve diffusion flow of closed plane curves
• Asymptotics for a class of non-linear evolution equations, with applications to geometric problems
• Curve-straightening in Riemannian manifolds
• \(L^ 2\) flow of curve straightening in the plane
• Curve straightening flow deforms closed plane curves with nonzero rotation number to circles
• Curve straightening and a minimax argument for closed elastic curves
• Higher chain formula proved by combinatorics
• Evolution of Elastic Curves in $\Rn$: Existence and Computation
• The affine curve-lengthening flow
• A note on quasilinear parabolic equations on manifolds
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