The Maximum Modulus Theorem for Holomorphic Functions

We prove the Maximum Modulus Principle for Holomorphic Functions. If we are given a holomorphic function on a open connected set, then if there is a point in the set where the maximum is attained (in modulus), then the function must be constant. We use the Cauchy formula together with the identity principle for holomorphic functions to prove this result which has a tremendous number of applications.

#mikethemathematician, #mikedabkowski, #profdabkowski, #complexanalysis, #maximumprinciple

[punditgi]

Maximum math is right here on this channel. 😊