Complex analysis modulus principle

What is the maximum modulus principle for harmonic functions?

Theorem (Maximum Modulus Theorem for Harmonic Functions).
If D is a bounded domain, u is harmonic in D and continuous on D, and u ≤ M on u220.

1. D: then u ≤ M on D.
That is, u attains its maximum on the boundary u220.
2. D

What is the minimum modulus principle?

Minimum Modulus principle If f is a non-constant holomorphic function a bounded region G and continuous on \xafG, then either f has a zero in G or f assumes its minimum value on u220.

1. G

What is the modulus theorem in complex analysis?

According to the Maximum Modulus Theorem in complex analysis, if a non-constant function/(z) is continuous on a closed bounded region R and is analytic at every interior point of R, then the maximum value of \\f (z) in R must occur on the boundary of R..

1. G
._{May 21, 2015}