A variational construction of Hamiltonian stationary surfaces with isolated Schoen–Wolfson conical singularities

We construct using variational methods Hamiltonian stationary surfaces with isolated Schoen–Wolfson conical singularities. We obtain these surfaces through a convergence process reminiscent to the Ginzburg–Landau asymptotic analysis in the strongly repulsive regime introduced by Bethuel, Brezis and Hélein. We describe in particular how the prescription of Schoen–Wolfson conical singularities is related to optimal Wente constants.