The elastica problem under area constraint

DOI10.1007/s00208-015-1284-yzbMath1345.49049arXiv1411.6100OpenAlexW1926479504MaRDI QIDQ303585

Vincenzo Ferone, Carlo Nitsch, Bernhard Kawohl

Publication date: 22 August 2016

Published in: Mathematische Annalen (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1411.6100

zbMATH Keywords

minimizationelastic energyclosed curvesarea constraint

Mathematics Subject Classification ID

Optimization of shapes other than minimal surfaces (49Q10) Inequalities and extremum problems in real or complex geometry (51M16)

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Cites Work

• Unnamed Item
• The total squared curvature of curves and approximation by piecewise circular curves
• Plane domains which are spectrally determinded. II
• Closed Euler elasticae
• The total squared curvature of closed curves
• An isoperimetric inequality with applications to curve shortening
• The heat equation shrinking convex plane curves
• The asymptotics of the heat equation for a boundary value problem
• Closed curves in \(E^ 2\) and \(S^ 2\) whose total squared curvatures are almost minimal
• Plane domains which are spectrally determined
• A new isoperimetric inequality for the elasticae
• Elasticae in a Riemannian submanifold
• Curve straightening flow deforms closed plane curves with nonzero rotation number to circles
• Application of Andrews and Green-Osher inequalities to nonlocal flow of convex plane curves
• Curve straightening and a minimax argument for closed elastic curves
• Euler elasticae in the plane and the Whitney-Graustein theorem
• Evolution of Elastic Curves in $\Rn$: Existence and Computation
• Elastic energy of a convex body
• Curves in the Hyperbolic Plane and mean Curvature of Tori in 3-Space
• The influence of elasticity on analysis: The classic heritage
• Confined Elastic Curves
• Knotted Elastic Curves in R ³
• Bonnesen-Style Isoperimetric Inequalities
• Curve-straightening and the Palais-Smale condition
• Positive Centers and the Bonnesen Inequality
• Minimal surfaces bounded by elastic lines
• The motion of elastic planar closed curves under the area-preserving condition