Physical Interpretation
A physical interpretation of this principle comes from the heat equation. That is, since log |f(z)| is harmonic, it is thus the steady state of a heat flow on the region D. Suppose a strict maximum was attained on the interior of D, the heat at this maximum would be dispersing to the points around it, which would contradict the assumption that this represents the steady state of a system.
Read more about this topic: Maximum Modulus Principle
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