# Definition:Teichmüller Annulus

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## Definition

Let $R \in \R_{>0}$.

The set:

- $A := \C \setminus \paren {\closedint{-1} 0 \cup \hointr R {+\infty} }$

is a **Teichmüller annulus**.

The modulus of $A$ is denoted $\map \Lambda R$.

## Also known as

A **Teichmüller annulus** is also sometimes found referred to as a **Teichmüller extremal domain**.

## Also see

- Teichmüller Modulus Theorem: among all annuli that separate the two points $0$ and $-1$ both from $\infty$ and from a point $z \in \C$ with $\cmod z = R$, the
**Teichmüller annulus**has the greatest modulus.

- Definition:Grötzsch Annulus: a related concept

## Source of Name

This entry was named for Oswald Teichmüller.