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.

The modulus of $A$ is denoted $\Lambda \left({R}\right)$.

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 $\left|{z}\right| = R$, the Teichmüller annulus has the greatest modulus.


 * Definition:Grötzsch Annulus: a related concept