Homotopy classes of self-maps of annuli, generalised twists and spin degree

DOI10.1007/s00205-009-0280-3zbMath1207.55004OpenAlexW2042390135MaRDI QIDQ993334

Ali Taheri

Publication date: 10 September 2010

Published in: Archive for Rational Mechanics and Analysis (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00205-009-0280-3

zbMATH Keywords

nonlinear elasticityenumeration problem for homotopy classesgeneralised annulustwist solution

Mathematics Subject Classification ID

Nonlinear elasticity (74B20) Degree, winding number (55M25) Homotopy theory (55P99) Lagrange's equations (70H03)

Related Items (17)

On a class of stationary loops on \(\mathbf{SO}(n)\) and the existence of multiple twisting solutions to a nonlinear elliptic system subject to a hard incompressibility constraint ⋮ \(\sigma_2\)-energy as a polyconvex functional on a space of self-maps of annuli in the multi-dimensional calculus of variations ⋮ Whirl mappings on generalised annuli and the incompressible symmetric equilibria of the Dirichlet energy ⋮ On multiple solutions to a family of nonlinear elliptic systems in divergence form coupled with an incompressibility constraint ⋮ Geodesics on \(\mathrm{SO}(n)\) and a class of spherically symmetric maps as solutions to a nonlinear generalised harmonic map problem ⋮ Topology of twists, extremising twist paths and multiple solutions to the nonlinear system in variation \(\mathscr{L}[u = \nabla \mathscr{P}\)] ⋮ Spherical twists, stationary paths and harmonic maps from generalised annuli into spheres ⋮ On Weyl's asymptotics and remainder term for the orthogonal and unitary groups ⋮ Annular rearrangements, incompressible axi-symmetric whirls and \(L^1\)-local minimisers of the distortion energy ⋮ The interplay between two Euler-Lagrange operators relating to the nonlinear elliptic system \(\Sigma [(u, {\mathscr{P}}), \varOmega\)] ⋮ On the uniqueness and monotonicity of energy minimisers in the homotopy classes of incompressible mappings and related problems ⋮ Twist maps as energy minimisers in homotopy classes: symmetrisation and the coarea formula ⋮ An infinite scale of incompressible twisting solutions to the nonlinear elliptic system \(\mathcal{L} [u; \mathsf{A}, \mathsf{B} = \nabla \mathcal{P}\) and the discriminant \(\varDelta(h, g)\)] ⋮ GENERALIZED TWISTS AS ELASTIC ENERGY EXTREMALS ON ANNULI, QUATERNIONS AND LIFTING TWIST LOOPS TO THE SPINOR GROUPS ⋮ On critical points of the \(\sigma_2\)-energy over a space of measure preserving maps ⋮ Stability and local minimality of spherical harmonic twists \(u={\mathbf{Q}}(|x|) x|x|^{-1} \), positivity of second variations and conjugate points on \(\mathbf{SO}(n)\) ⋮ On the existence and multiplicity of topologically twisting incompressible $H$-harmonic maps and a structural H-condition

Cites Work

• Local minimizers and quasiconvexity -- the impact of topology
• Generalised twists, \(\mathrm {SO}(n)\), and the \(p\)-energy over a space of measure preserving maps
• Minimizing the Dirichlet energy over a space of measure preserving maps
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• Regularity properties of deformations with finite energy
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• On products in homotopy groups
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• Note on the Homotopy Properties of the Components of the Mapping Space X s p
• Polyconvexity, generalised twists and energy minimizers on a space of self-maps of annuli in the multi-dimensional calculus of variations
• The Homotopy Groups of a Space of Maps between Oriented Closed Surfaces
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