Minimal submanifolds from the abelian Higgs model

DOI10.1007/s00222-020-01000-6zbMath1467.53025arXiv1905.13726OpenAlexW3085121118MaRDI QIDQ2661168

Daniel Stern, Alessandro Pigati

Publication date: 1 April 2021

Published in: Inventiones Mathematicae (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1905.13726

zbMATH Keywords

varifoldsBochner identitiesself-dual Yang-Mills-Higgs energy

Mathematics Subject Classification ID

Yang-Mills and other gauge theories in quantum field theory (81T13) Special connections and metrics on vector bundles (Hermite-Einstein, Yang-Mills) (53C07) Differential geometry of immersions (minimal, prescribed curvature, tight, etc.) (53C42)

Related Items (13)

The viscosity method for min-max free boundary minimal surfaces ⋮ The Yang-Mills-Higgs functional on complex line bundles: \(\Gamma\)-convergence and the London equation ⋮ Entire solutions to 4 dimensional Ginzburg-Landau equations and codimension 2 minimal submanifolds ⋮ The p-widths of a surface ⋮ Ginzburg-Landau equations on non-compact Riemann surfaces ⋮ Convergence of the self‐dual U(1)‐Yang–Mills–Higgs energies to the (n−2)$(n-2)$‐area functional ⋮ Multiplicity‐1 minmax minimal hypersurfaces in manifolds with positive Ricci curvature ⋮ On the bifurcation theory of the Ginzburg–Landau equations ⋮ Solutions of the Ginzburg–Landau equations concentrating on codimension‐2 minimal submanifolds ⋮ Stable solutions to the abelian Yang-Mills-Higgs equations on \(S^2\) and \(T^2\) ⋮ Topological singular set of vector-valued maps. II: \( \varGamma \)-convergence for Ginzburg-Landau type functionals ⋮ Topological singularities for vector-valued Sobolev maps and applications ⋮ A comparison of the Almgren-Pitts and the Allen-Cahn min-max theory

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