Editing Maximum modulus principle (section)

{{Short description|Mathematical theorem in complex analysis}}
{{Redirect-distinguish|Maximal principle|Hausdorff maximal principle}}
[[Image:Maximum modulus principle.png|right|thumb|A plot of the modulus of <math>\cos(z)</math> (in red) for <math>z</math> in the [[unit disk]] centered at the origin (shown in blue). As predicted by the theorem, the maximum of the modulus cannot be inside of the disk (so the highest value on the red surface is somewhere along its edge).]]
In [[mathematics]], the '''maximum modulus principle''' in [[complex analysis]] states that if <math>f</math> is a [[holomorphic function]], then the [[absolute value|modulus]] 
<math>|f|</math> cannot exhibit a strict [[maximum]] that is strictly within the [[domain of a function|domain]] of <math>f</math>. 

In other words, either <math>f</math> is locally a [[constant function]], or, for any point <math>z_0</math> inside the domain of <math>f</math> there exist other points arbitrarily close to <math>z_0</math> at which <math>|f|</math> takes larger values.