In mathematics, the maximum modulus principle in complex analysis states that if f is a holomorphic function, then the modulus cannot exhibit a true local maximum that is properly within the domain of f.
In other words, either f is a constant function, or, for any point z0 inside the domain of f there exist other points arbitrarily close to z0 at which |f | takes larger values.
Read more about Maximum Modulus Principle: Formal Statement, Sketch of The Proof, Physical Interpretation, Applications
Famous quotes containing the words maximum and/or principle:
“Probably the only place where a man can feel really secure is in a maximum security prison, except for the imminent threat of release.”
—Germaine Greer (b. 1939)
“A certain secret jealousy of the British Minister is always lurking in the breast of every American Senator, if he is truly democratic; for democracy, rightly understood, is the government of the people, by the people, for the benefit of Senators, and there is always a danger that the British Minister may not understand this political principle as he should.”
—Henry Brooks Adams (1838–1918)