The parabolic $U(1)$-Higgs equations and codimension-two mean curvature flows

Special connections and metrics on vector bundles (Hermite-Einstein, Yang-Mills) (53C07) Methods of global Riemannian geometry, including PDE methods; curvature restrictions (53C21) Flows related to mean curvature (53E10)

Cites Work

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Geometry of measures in $R^ n:$ Distribution, rectifiability, and densities
A local regularity theorem for mean curvature flow
Asymptotic behavior for singularities of the mean curvature flow
The effect of a singular perturbation on nonconvex variational problems
On the equivalence of the first and second order equations for gauge theories
Arbitrary N-vortex solutions to the first order Ginzburg-Landau equations
Motion by mean curvature as the singular limit of Ginzburg-Landau dynamics
Motion of level sets by mean curvature. III
Monotonicity formulas for parabolic flows on manifolds
Invariant connections and vortices
Convergence of the Allen-Cahn equation to Brakke's motion by mean curvature
The Jacobian and the Ginzburg-Landau energy
The Allen-Cahn equation on closed manifolds
Min-max for phase transitions and the existence of embedded minimal hypersurfaces
From constant mean curvature hypersurfaces to the gradient theory of phase transitions.
Special Lagrangians, stable bundles and mean curvature flow
Integrality of varifolds in the singular limit of reaction-diffusion equations
Complex Ginzburg-Landau equations in high dimensions and codimension two area minimizing currents
Convergence of phase interfaces in the van der Waals-Cahn-Hilliard theory.
Minimal surfaces and the Allen-Cahn equation on 3-manifolds: index, multiplicity, and curvature estimates
Convergence of the parabolic Ginzburg-Landau equation to motion by mean curvature
Vortices in holomorphic line bundles over closed Kähler manifolds
Minimal submanifolds from the abelian Higgs model
Stable phase interfaces in the van der Waals–Cahn–Hilliard theory
Phase transitions and generalized motion by mean curvature
Off diagonal short time asymptotics for fundamental solution of diffusion equation
The Motion of a Surface by Its Mean Curvature. (MN-20)
Elliptic regularization and partial regularity for motion by mean curvature
Asymptotics for the Ginzburg-Landau equation in arbitrary dimensions
The p-widths of a surface
Convergence of the self‐dual U(1)‐Yang–Mills–Higgs energies to the (n−2)$(n-2)$‐area functional
Solutions of the Ginzburg–Landau equations concentrating on codimension‐2 minimal submanifolds

The parabolic \(U(1)\)-Higgs equations and codimension-two mean curvature flows