Lagrangian approximation of totally real concordances

Abstract We show that a two‐dimensional totally real concordance can be approximated by a Lagrangian concordance whose Legendrian boundary has been stabilised both positively and negatively sufficiently many times. The main applications that we provide are constructions of knotted Lagrangian concordances in arbitrary four‐dimensional symplectisations, as well as of knotted Lagrangian tori in symplectisations of overtwisted contact three‐manifolds.