Definition:Teichmüller Annulus

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

The set:
 * $A := \C \setminus \left({\left[{-1 \,.\,.\, 0}\right] \cup \left[{R \,.\,.\, +\infty}\right)}\right)$

is a Teichmüller annulus (or also Teichmüller extremal domain).

The modulus of $A$ is denoted $\Lambda(R)$.

Properties
By the 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 $|z|=R$, the Teichmüller annulus has the greatest modulus.

The Teichmüller annulus is closely related to the Grötzsch annulus.