Abstract
We prove a sharp Schwarz lemma type inequality for the Weierstrass–Enneper parameterization of minimal disks. It states the following. If F:D→Σ is a conformal harmonic parameterization of a minimal disk Σ⊂R3, where D is the unit disk and |Σ|=πR2, then |Fx(z)|(1−|z|2)≤R. If for some z the previous inequality is equality, then the surface is an affine image of a disk, and F is linear up to a Möbius transformation of the unit disk.
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