Complex Structure
In complex analysis an annulus ann(a; r, R) in the complex plane is an open region defined by:
If r is 0, the region is known as the punctured disk of radius R around the point a.
As a subset of the complex plane, an annulus can be considered as a Riemann surface. The complex structure of an annulus depends only on the ratio r/R. Each annulus ann(a; r, R) can be holomorphically mapped to a standard one centered at the origin and with outer radius 1 by the map
The inner radius is then r/R < 1.
The Hadamard three-circle theorem is a statement about the maximum value a holomorphic function may take inside an annulus.
Read more about this topic: Annulus (mathematics)
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