13 citations · 15 across the 4 of their papers we have counts for
6 papers · 1 filter
Nonabelian Yang-Mills-Higgs and Plateau's problem in codimension three
Davide Parise, Alessandro Pigati, Daniel Stern
We investigate the asymptotic behavior of the -Yang-Mills-Higgs energy in the large mass limit, proving convergence to the codimensi…
The Parabolic -Higgs Equations and Codimension-two Mean Curvature Flows
Davide Parise, Alessandro Pigati, Daniel Stern
We develop the asymptotic analysis as for the natural gradient flow of the self-dual -Higgs energies $$E_ε(u,\nabla)=\int_M\left(|\nabla u|^2+ε^2|F_{\nabla}|^2+\frac…
Non-degenerate minimal submanifolds as energy concentration sets: a variational approach
Guido De Philippis, Alessandro Pigati
We prove that every non-degenerate minimal submanifold of codimension two can be obtained as the energy concentration set of a family of critical maps for the (rescaled) Ginzburg-L…
Convergence of the self-dual -Yang-Mills-Higgs energies to the -area functional
Davide Parise, Alessandro Pigati, Daniel Stern
Given a hermitian line bundle on a closed Riemannian manifold , the self-dual Yang-Mills-Higgs energies are a natural family of functionals \begin{align*} &E_ε(u,…
The viscosity method for min-max free boundary minimal surfaces
Alessandro Pigati
We adapt the viscosity method introduced by Rivière to the free boundary case. Namely, given a compact oriented surface , possibly with boundary, a closed ambient Riemannian man…
Minimal submanifolds from the abelian Higgs model
Alessandro Pigati, Daniel Stern
Given a Hermitian line bundle over a closed, oriented Riemannian manifold , we study the asymptotic behavior, as , of couples critical for the…