A class of extremising sphere-valued maps with inherent maximal tori symmetries in \(\mathbf{SO}(n)\)

DOI10.1186/s13661-017-0917-3zbMath1384.49005OpenAlexW2778742089WikidataQ59612548 ScholiaQ59612548MaRDI QIDQ1689780

Ali Taheri, Stuart Day

Publication date: 17 January 2018

Published in: Boundary Value Problems (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1186/s13661-017-0917-3

zbMATH Keywords

symmetries\(\mathbf{SO}(n)\)generalized sphere-valued harmonic mapsmaximal tori and conjugacysecond energy variationsspherical whirls

Mathematics Subject Classification ID

Existence theories for free problems in two or more independent variables (49J10) Variational methods for elliptic systems (35J50) Boundary value problems for second-order elliptic systems (35J57)

Related Items

Whirl mappings on generalised annuli and the incompressible symmetric equilibria of the Dirichlet energy ⋮ 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 \(\mathscr{L}[u = \nabla \mathscr{P}\)] ⋮ The interplay between two Euler-Lagrange operators relating to the nonlinear elliptic system \(\Sigma [(u, {\mathscr{P}}), \varOmega\)] ⋮ 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 \(\varDelta(h, g)\)] ⋮ 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

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Spherical twists, stationary paths and harmonic maps from generalised annuli into spheres
• Local minimizers and quasiconvexity -- the impact of topology
• Stability and local minimality of spherical harmonic twists \(u={\mathbf{Q}}(|x|) x|x|^{-1} \), positivity of second variations and conjugate points on \(\mathbf{SO}(n)\)
• Stability and uniqueness properties of the equator map from a ball into an ellipsoid
• The approximation problem for Sobolev maps between two manifolds
• Geodesics on \(\mathrm{SO}(n)\) and a class of spherically symmetric maps as solutions to a nonlinear generalised harmonic map problem
• Annular rearrangements, incompressible axi-symmetric whirls and \(L^1\)-local minimisers of the distortion energy
• Strong versus weak local minimizers for the perturbed Dirichlet functional
• The minimality of the map \(\frac{x}{\| x \|}\) for weighted energy
• Sufficiency theorems for local minimizers of the multiple integrals of the calculus of variations
• SPHERICAL TWISTS, SO(n) AND THE LIFTING OF THEIR TWIST PATHS TO Spin(n) IN LOW DIMENSIONS
• Another Report on Harmonic Maps
• Minimizing p-harmonic maps into spheres.
• A Report on Harmonic Maps
• Function Spaces and Partial Differential Equations
• Harmonic maps
• Topology and Sobolev spaces
• Topology of Sobolev mappings
• On the minimality of the \(p\)-harmonic map \(\frac{x}{|x|}:B^n\to S^{n-1}\)