On the bifurcation theory of the Ginzburg–Landau equations

DOI10.1090/proc/16510zbMath1529.35487arXiv2210.03271OpenAlexW4366404109MaRDI QIDQ6183382

Goncalo Oliveira, Ákos Nagy

Publication date: 4 January 2024

Full work available at URL: https://arxiv.org/abs/2210.03271

zbMATH Keywords

bifurcation theoryGinzburg-Landau equationsnonminimal solutions

Mathematics Subject Classification ID

Special connections and metrics on vector bundles (Hermite-Einstein, Yang-Mills) (53C07) Bifurcations in context of PDEs (35B32) Variational problems concerning extremal problems in several variables; Yang-Mills functionals (58E15) Ginzburg-Landau equations (35Q56) Bifurcation theory for PDEs on manifolds (58J55)

Cites Work

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• Non-minimal Yang-Mills fields and dynamics
• A Morse theory for equivariant Yang-Mills
• Invariant connections and vortices
• Uhlenbeck compactness
• Irreducible Ginzburg-Landau fields in dimension 2
• Bifurcation theory of functional differential equations
• Ginzburg-Landau equations on Riemann surfaces of higher genus
• Vortices in holomorphic line bundles over closed Kähler manifolds
• Minimal submanifolds from the abelian Higgs model
• Convergence of the self‐dual U(1)‐Yang–Mills–Higgs energies to the (n−2)$(n-2)$‐area functional

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