A new isoperimetric inequality for the elasticae

DOI10.4171/JEMS/740zbMath1377.49047arXiv1412.4536MaRDI QIDQ1676086

Antoine Henrot, Dorin Bucur

Publication date: 3 November 2017

Published in: Journal of the European Mathematical Society (JEMS) (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1412.4536

zbMATH Keywords

isoperimetric inequalitycurvatureEuler elasticaeminimization of elastic energy

Mathematics Subject Classification ID

Classical linear elasticity (74B05) Optimization of shapes other than minimal surfaces (49Q10) Curves in Euclidean and related spaces (53A04) Inequalities and extremum problems in real or complex geometry (51M16)

Related Items (10)

Geometric inequalities involving mean curvature for closed surfaces ⋮ An efficient diffusion generated motion method for wetting dynamics ⋮ The elastica problem under area constraint ⋮ On the maximal mean curvature of a smooth surface ⋮ Existence, regularity and structure of confined elasticae ⋮ An estimate for the anisotropic maximum curvature in the planar case ⋮ Some minimization problems for planar networks of elastic curves ⋮ Elasticae and inradius ⋮ Quantitative estimates for bending energies and applications to non-local variational problems ⋮ Elastic curves and phase transitions

Cites Work

• Unnamed Item
• The elastica problem under area constraint
• Closed Euler elasticae
• An isoperimetric inequality with applications to curve shortening
• Curve straightening and a minimax argument for closed elastic curves
• Variational methods in shape optimization problems
• Variation and optimization of formes. A geometric analysis
• Elastic energy of a convex body
• Classification of limiting shapes for isotropic curve flows

This page was built for publication: A new isoperimetric inequality for the elasticae