Definition:Grötzsch Annulus

Definition
Let $R \in \R_{>1}$.

The set:
 * $A := \left\{{z \in \C: \left \vert {z}\right \vert > 1 \text{ and } z \notin \left[{R \,.\,.\, +\infty}\right)}\right \}$

is called a Grötzsch annulus.

Also known as
A Grötzsch annulus can also seen referred to as a Grötzsch extremal domain.

Also see

 * Grötzsch Modulus Theorem: among all annuli that separate the unit circle from the points $R$ and $\infty$, the Grötzsch annulus has the greatest modulus.


 * Definition:Teichmüller Annulus, which is closely related.