Degree 3 Algebraic Minimal Surfaces in the 3-Sphere

We give a local analytic characterization that a minimal surface in the 3-sphere S3 ⊂ 4 defined by an irreducible cubic polynomial is one of the Lawson's minimal tori. This provides an alternative proof of the result by Perdomo (Characterization of order 3 algebraic immersed minimal surfaces of S3, Geom. Dedicata 129 (2007), 23–34).