The Yang-Mills-Higgs functional on complex line bundles: \(\Gamma\)-convergence and the London equation

DOI10.1007/s00205-023-01933-1arXiv2206.03327OpenAlexW4387449561MaRDI QIDQ6077259

Giandomenico Orlandi, Giacomo Canevari, Federico Luigi Dipasquale

Publication date: 17 October 2023

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

Full work available at URL: https://arxiv.org/abs/2206.03327

Mathematics Subject Classification ID

Variational problems concerning extremal problems in several variables; Yang-Mills functionals (58E15) Global differential geometry (53Cxx) Manifolds and measure-geometric topics (49Qxx)

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Dynamics of Ginzburg-Landau and Gross-Pitaevskii vortices on manifolds
• Vortices in the magnetic Ginzburg-Landau model
• Special metrics and stability for holomorphic bundles with global sections
• Density of smooth functions between two manifolds in Sobolev spaces
• A note on the Hodge theory for functionals with linear growth
• Invariant connections and vortices
• Renormalized energy for Ginzburg-Landau vortices on closed surfaces
• Lower bounds for the energy of unit vector fields and applications
• A product estimate for Ginzburg-Landau and application to the gradient-flow
• Functions with prescribed singularities
• Uhlenbeck compactness
• Nonlinear Hodge theory on manifolds with boundary
• Linear and nonlinear aspects of vortices. The Ginzburg-Landau model
• Codimension one minimal cycles with coefficients in \(Z\) or \(Z_p\), and variational functionals on fibered spaces
• The Jacobian and the Ginzburg-Landau energy
• Covariant Schrödinger semigroups on Riemannian manifolds
• Cycles of least mass in a Riemannian manifold, described through the ``phase transition energy of the sections of a line bundle
• Motion of concentration sets in Ginzburg-Landau equations.
• Hodge decomposition. A method for solving boundary value problems
• Vortices for a variational problem related to superconductivity
• Regular stationary solutions of the cylindrically symmetric Einstein-matter-gauge equations
• Defects in semilinear wave equations and timelike minimal surfaces in Minkowski space
• Stable solutions to the abelian Yang-Mills-Higgs equations on \(S^2\) and \(T^2\)
• Existence and limiting behavior of min-max solutions of the Ginzburg-Landau equations on compact manifolds
• Structural descriptions of limits of the parabolic Ginzburg-Landau equation on closed manifolds
• Time-like minimal submanifolds as singular limits of nonlinear wave equations
• Convergence of the parabolic Ginzburg-Landau equation to motion by mean curvature
• Vortices in holomorphic line bundles over closed Kähler manifolds
• Renormalized energy between vortices in some Ginzburg-Landau models on 2-dimensional Riemannian manifolds
• Minimal submanifolds from the abelian Higgs model
• Lorentzian varifolds and applications to relativistic strings
• Anti Self-Dual Yang-Mills Connections Over Complex Algebraic Surfaces and Stable Vector Bundles
• Convergence of minimizers with local energy bounds for the Ginzburg-Landau functionals
• Analysis and Approximation of the Ginzburg–Landau Model of Superconductivity
• Lower Bounds for Generalized Ginzburg--Landau Functionals
• Uniform estimates for the parabolic Ginzburg–Landau equation
• Functions of bounded higher variation
• On the existence of hermitian-yang-mills connections in stable vector bundles
• L p Theory of Differential Forms on Manifolds
• ASYMPTOTIC BEHAVIOR OF THE GINZBURG-LANDAU FUNCTIONAL ON COMPLEX LINE BUNDLES OVER COMPACT RIEMANN SURFACES
• Elementary Differential Topology. (AM-54)
• Variational convergence for functionals of Ginzburg-Landau type
• Theory of Superconductivity
• Ginzburg-Landau vortices
• Riemannian geometry and geometric analysis
• Asymptotics for the Ginzburg-Landau equation in arbitrary dimensions
• Dynamics of Ginzburg-Landau vortices for vector fields on surfaces