# Definition:Grötzsch Annulus

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## Definition

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

The set:

- $A := \set {z \in \C: \cmod z > 1 \text{ and } z \notin \hointr R {+\infty} }$

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.

## Source of Name

This entry was named for Camillo Herbert Grötzsch.