Abstract
Let Ω ⊂ C2 be a smooth domain. We establish conditions under which a weakly conformal, branched Ω -free boundary Hamiltonian stationary Lagrangian immersion u of a disc in C2 is a Ω -free boundary minimal immersion. We deduce that if u is a weakly conformal, branched B1(0) -free boundary Hamiltonian stationary Lagrangian immersion of a disc with Legendrian boundary, then u(D2) is a Lagrangian equatorial plane disc. Furthermore, we present examples of Ω -free boundary Hamiltonian stationary discs, demonstrating the optimality of our assumptions.