Curve straightening and a minimax argument for closed elastic curves
Copyright policy )Curve straightening and a minimax argument for closed elastic curves
The authors study the functional \(F=\oint k^ 2 ds\) (''total squared curvature'') on the space of smooth closed curves in \({\mathbb{R}}^ 3\) of fixed length. In particular they establish the Palais-Smale condition for F, so the gradient flow of F (''curve straightening'') is well-behaved. As an application all critical points of F (''closed elastic curves'') are classified by a minimax argument.
- Max Planck Society Germany
- Case Western Reserve University United States
total squared curvature'', Curves in Euclidean and related spaces, closed elastic curves'', Palais-Smale condition, closed curves, Geometry and Topology, Variational problems in applications to the theory of geodesics (problems in one independent variable)
total squared curvature'', Curves in Euclidean and related spaces, closed elastic curves'', Palais-Smale condition, closed curves, Geometry and Topology, Variational problems in applications to the theory of geodesics (problems in one independent variable)
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