# Definition:Teichmüller Annulus

## 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.

## Source of Name

This entry was named for Oswald Teichmüller.