Definition:Grötzsch Annulus

Definition
Let $$ R > 1 $$. The set
 * $$A := \{z\in\C: |z|>1 \text{ and } z\notin [R,\infty) \}$$

is called a Grötzsch annulus (or also Grötzsch extremal domain).

The modulus of $$A$$ is denoted $$M(R)$$.

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

The Grötzsch annulus is closely related to the Teichmüller annulus.