Asymptotics for minimizers of the Ginzburg–Landau energy with optimal regularity of the boundary data and applications

We perform the classical asymptotic analysis for the Ginzburg–Landau energy which originates from the celebrated paper by Bethuel, Brezis, Hélein for nonsmooth boundary data. More precisely, we give optimal regularity assumptions on the boundary curve of planar domains and Dirichlet boundary data on them. When the Dirichlet boundary data is the tangent vector field of the boundary curve, our framework allows us to define a natural energy minimizing frame for simply connected domains enclosing Weil–Petersson curves.