Knotted Elastic Curves in R 3
From MaRDI portal
Publication:3726905
DOI10.1112/jlms/s2-30.3.512zbMath0595.53001OpenAlexW2070338430MaRDI QIDQ3726905
David A. Singer, Joel C. Langer
Publication date: 1984
Published in: Journal of the London Mathematical Society (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1112/jlms/s2-30.3.512
Related Items (67)
Surface constrained elastic rods with application to the sphere ⋮ Torus knots and polynomial invariants for a class of soliton equations ⋮ Structure and classification results for the ∞-elastica problem ⋮ Massless particles in three-dimensional Lorentzian warped products ⋮ The elastica problem under area constraint ⋮ A differential-geometric interpretation of Kirchhoff’s elastic rods ⋮ On the Cauchy Problem for a Dynamical Euler's Elastica ⋮ Existence, regularity and structure of confined elasticae ⋮ Unnamed Item ⋮ F-actin bending facilitates net actomyosin contraction by inhibiting expansion with plus-end-located myosin motors ⋮ Elastica as a dynamical system ⋮ Extendability of Kirchhoff elastic rods in complete Riemannian manifolds ⋮ Curvature-dependent energies minimizers and visual curve completion ⋮ Existence of free nonclosed Euler–Bernoulli elastica ⋮ Local geometric invariants of integrable evolution equations ⋮ On a flow to untangle elastic knots ⋮ On relaxed elastic lines of the second type on an oriented surface in the Galilean space \(G_3\) ⋮ Kirchhoff elastic rods in five-dimensional space forms whose centerlines are not helices ⋮ Rolling sphere problems on spaces of constant curvature ⋮ Li-Yau type inequality for curves in any codimension ⋮ Extremal curves for weighted elastic energy in surfaces of 3-space forms ⋮ A new flow on starlike curves in $\mathbb {R}^3$ ⋮ A gradient flow for the \(p\)-elastic energy defined on closed planar curves ⋮ A Li-Yau inequality for the 1-dimensional Willmore energy ⋮ Willmore energy estimates in conformal Berger spheres ⋮ On the curve straightening flow of inextensible, open, planar curves ⋮ General helices and a theorem of Lancret ⋮ The \(p\)-elastic flow for planar closed curves with constant parametrization ⋮ Euler elasticae in the plane and the Whitney-Graustein theorem ⋮ Reduction of variables for Willmore-Chen submanifolds in seven spheres ⋮ Nonlinear dynamics of filaments. I: Dynamical instabilities ⋮ A note on a Bäcklund transformation for the continuous Heisenberg model ⋮ Kirchhoff elastic rods in three-dimensional space forms ⋮ Magnetic vortex filament flows ⋮ Unit speed stationary points of the acceleration ⋮ Some Variational Problems on Curves and Applications ⋮ Dynamics of charges and solitons ⋮ QUADRATIC CURVATURE ENERGIES IN THE 2-SPHERE ⋮ Explicit formulas, symmetry and symmetry breaking for Willmore surfaces of revolution ⋮ The elastic trefoil is the doubly covered circle ⋮ Critical curves for a Santaló problem in 3-space forms ⋮ Willmore tori in a wide family of conformal structures on odd dimensional spheres ⋮ A new approach for magnetic curves in 3D Riemannian manifolds ⋮ Kirchhoff elastic rods in higher-dimensional space forms ⋮ A note on the \(p\)-elastica in a constant sectional curvature manifold ⋮ Extremals of curvature energy actions on spherical closed curves ⋮ On the geometry of stiff knots ⋮ Symmetric soliton configurations of bosonic string theories ⋮ Matched asymptotic expansions for twisted elastic knots: a self-contact problem with non-trivial contact topology ⋮ Minimizing configurations for elastic surface energies with elastic boundaries ⋮ Elastic curves with constant curvature at rest in the hyperbolic plane ⋮ The dynamics of elastic closed curves under uniform high pressure ⋮ Asymptotic behavior of the maximum of Jacobi's zeta function ⋮ Anisotropic bending energies of curves ⋮ The Hasimoto transformation and integrable flows on curves ⋮ Elastic curves and phase transitions ⋮ The critical points of the elastic energy among curves pinned at endpoints ⋮ Plateau’s Problem ⋮ Elliptic integral solutions of spatial elastica of a thin straight rod bent under concentrated terminal forces ⋮ Elastic knots in Euclidean 3-space ⋮ A group-theoretic approach to the geometry of elastic rings ⋮ Willmore tori and Willmore-Chen submanifolds in pseudo-Riemannian spaces ⋮ Solitons, Euler’s equation, and vortex patch dynamics ⋮ Optimal control on Lie groups and integrable Hamiltonian systems ⋮ On motion of an elastic wire in a Riemannian manifold and singular perturbation ⋮ Computing confined elasticae ⋮ Poisson geometry of the filament equation
This page was built for publication: Knotted Elastic Curves in R 3