Abstract: | We prove a sharp Schwarz lemma type inequality for the Weierstrass–Enneper parameterization of minimal disks. It states the following. If is a conformal harmonic parameterization of a minimal disk , where is the unit disk and , then . If for some the previous inequality is equality, then the surface is an affine image of a disk, and is linear up to a Möbius transformation of the unit disk. |