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math.DG2022★ 1 cited
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…
math.DG2022
Quantization and non-quantization of energy for higher-dimensional Ginzburg-Landau vortices
Alessandro Pigati, Daniel Stern
Given a family of critical points for the complex Ginzburg--Landau energies \begin{align*} &E_ε(u)=\int_{M}\left(\frac{|du|^2}{2}+\frac{(1-|u|^2)^2}{4ε^2}\ri…