Spherical twists, stationary paths and harmonic maps from generalised annuli into spheres

DOI10.1007/s00030-011-0119-0zbMath1256.58004OpenAlexW2041709900MaRDI QIDQ421138

Ali Taheri

Publication date: 23 May 2012

Published in: NoDEA. Nonlinear Differential Equations and Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00030-011-0119-0

zbMATH Keywords

Euler-Lagrange equationharmonic equation

Mathematics Subject Classification ID

Variational methods for elliptic systems (35J50) Harmonic maps, etc. (58E20) Geometric theory, characteristics, transformations in context of PDEs (35A30) Boundary value problems for second-order elliptic systems (35J57)

Related Items (8)

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 ⋮ 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 \(\mathscr{L}[u = \nabla \mathscr{P}\)] ⋮ A class of extremising sphere-valued maps with inherent maximal tori symmetries in \(\mathbf{SO}(n)\) ⋮ 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 ⋮ Twist maps as energy minimisers in homotopy classes: symmetrisation and the coarea formula ⋮ Stability and local minimality of spherical harmonic twists \(u={\mathbf{Q}}(|x|) x|x|^{-1} \), positivity of second variations and conjugate points on \(\mathbf{SO}(n)\)

Cites Work

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• Homotopy classes of self-maps of annuli, generalised twists and spin degree
• Partial regularity for stationary harmonic maps into spheres
• Convexity conditions and existence theorems in nonlinear elasticity
• Applications harmoniques de surfaces riemanniennes
• Everywhere discontinuous harmonic maps into spheres
• Elliptic partial differential equations of second order
• Infinite dimensional Morse theory and multiple solution problems
• Braids, Links, and Mapping Class Groups. (AM-82)
• A Report on Harmonic Maps

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