Superposition of generalized maximal immersions and its applications

We derive a variant of the Weierstrass–Enneper representation for generalized maximal immersions generated by a single harmonic function. We use this variant to construct examples of generalized maximal immersion from a single family. Subsequently, we proved a ‘superposition principle’ for generalized maximal immersions. It says that if we have given finitely many generalized maximal immersions, one can add their parametrizations to get another generalized maximal immersion under certain assumptions. We also study how the singularity of maxfaces behaves under superposition.