Definition:Grötzsch Annulus

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.

Sources

• 1973: L.V. Ahlfors: Conformal Invariants: Topics in Geometric Function Theory