= Minimum modulus principle
A nonconstant <holomorphic function> cannot have a positive interior local minimum of its modulus. Wherever it is nonzero, its reciprocal is holomorphic; a positive modulus minimum would give a modulus maximum of the reciprocal, contradicting the <maximum modulus principle>. Thus if a holomorphic function on a neighborhood of a closed disk has modulus at the center strictly smaller than its minimum boundary modulus, it has a zero inside the disk. Otherwise the <Cauchy estimate> applied to its reciprocal would give the opposite inequality.
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