Maximum Modulus Principle - Applications

Applications

The maximum modulus principle has many uses in complex analysis, and may be used to prove the following:

• The fundamental theorem of algebra.
• Schwarz's lemma, a result which in turn has many generalisations and applications in complex analysis.
• The Phragmén–Lindelöf principle, an extension to unbounded domains.
• The Borel–Carathéodory theorem, which bounds an analytic function in terms of its real part.