Curve-straightening and the Palais-Smale condition

DOI10.1090/S0002-9947-98-01977-1zbMath0921.58008OpenAlexW1509368593WikidataQ125582598 ScholiaQ125582598MaRDI QIDQ4211122

Anders Linnér

Publication date: 10 September 1998

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

Full work available at URL: https://doi.org/10.1090/s0002-9947-98-01977-1

zbMATH Keywords

Palais-Smale conditiongradient trajectoriescurve-straightening

Mathematics Subject Classification ID

Dynamics induced by flows and semiflows (37C10) Methods of global Riemannian geometry, including PDE methods; curvature restrictions (53C21) Variational problems in applications to the theory of geodesics (problems in one independent variable) (58E10)

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The elastica problem under area constraint ⋮ Morse theory for elastica ⋮ Curvature-dependent energies minimizers and visual curve completion ⋮ Polar tangential angles and free elasticae ⋮ Overhanging of membranes and filaments adhering to periodic graph substrates ⋮ Symmetrized curve-straightening. ⋮ Existence of planar curves minimizing length and curvature ⋮ \(L^2\)-flow of elastic curves with clamped boundary conditions ⋮ On the curve straightening flow of inextensible, open, planar curves ⋮ Closed generalized elastic curves in \({\mathbf S}^{2}\)(1). ⋮ On the convergence of the elastic flow in the hyperbolic plane ⋮ QUADRATIC CURVATURE ENERGIES IN THE 2-SPHERE ⋮ Extremals of curvature energy actions on spherical closed curves ⋮ Elastic curves with constant curvature at rest in the hyperbolic plane ⋮ Elastic splines III: existence of stable nonlinear splines ⋮ Numerical approximation of boundary value problems for curvature flow and elastic flow in Riemannian manifolds ⋮ Elastic curves and phase transitions

Cites Work

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• The total squared curvature of closed curves
• Curve-straightening in Riemannian manifolds
• Geodesics on \(S^ 2\) and periodic points of annulus homeomorphisms
• Critical point theory and submanifold geometry
• Unified representations of nonlinear splines
• Curve straightening and a minimax argument for closed elastic curves
• Morse theory on Hilbert manifolds
• Some Properties of the Curve Straightening Flow in the Plane
• Existence of free nonclosed Euler–Bernoulli elastica

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