Definition:Grötzsch Annulus
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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.