Euler elasticae in the plane and the Whitney-Graustein theorem

DOI10.1134/S1061920813030011zbMath1287.57004arXiv1303.0443MaRDI QIDQ2441296

Yanyan Li

Publication date: 24 March 2014

Published in: Russian Journal of Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1303.0443

Mathematics Subject Classification ID

Curves in Euclidean and related spaces (53A04) Variational problems in applications to the theory of geodesics (problems in one independent variable) (58E10) Existence theories in calculus of variations and optimal control (49J99)

Related Items (11)

Theory of thickened knots ⋮ The elastica problem under area constraint ⋮ Existence, regularity and structure of confined elasticae ⋮ Remembering Patrick Dehornoy ⋮ Energy functionals and normal forms of knots and plane curves ⋮ Confined elasticae and the buckling of cylindrical shells ⋮ Bringing closed polygonal curves in the plane to normal form via local moves ⋮ Normal forms of unknotted ribbons and DNA ⋮ Elastic curves and phase transitions ⋮ The critical points of the elastic energy among curves pinned at endpoints ⋮ On the normal form of knots

Cites Work

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• Normal forms of twisted wire knots
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• [https://portal.mardi4nfdi.de/wiki/Publication:3740681 Reduction for Constrained Variational Problems and � κ 2 2 ds]
• Methodus inveniendi lineas curvas maximi minimive proprietate gaudentes, sive solutio problematis isoperimetrici lattissimo sensu accepti
• Torus Knots Extremizing the Möbius Energy

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