Minimal Lagrangian surfaces in CP² via the loop group method Part II: The general case

We extend the techniques introduced in {DoMaB1} for contractible Riemann surfaces to construct minimal Lagrangian immersions from arbitrary Riemann surfaces into CP² via the loop group method. Based on the potentials of translationally equivariant minimal Lagrangian surfaces, we introduce perturbed equivariant minimal Lagrangian surfaces in CP² and construct a class of minimal Lagrangian cylinders. Furthermore, we show that these minimal Lagrangian cylinders approximate Delaunay cylinders with respect to some weighted Wiener norm of the twisted loop group Λ SU(3)σ.