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

Abstract

We extend the techniques introduced in [10] for contractible Riemann surfaces to construct minimal Lagrangian immersions from arbitrary Riemann surfaces into the complex projective plane $C{P}^2$ via the loop group method. Based on the potentials of translationally equivariant minimal Lagrangian surfaces, we introduce perturbed equivariant minimal Lagrangian surfaces in $C{P}^2$ 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 $\Lambda SU{\left(3\right)}_{\sigma }$.