The simplest example for the non-innerness of the Carathéodory distance (Q921199)
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scientific article; zbMATH DE number 4165307
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | The simplest example for the non-innerness of the Carathéodory distance |
scientific article; zbMATH DE number 4165307 |
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The simplest example for the non-innerness of the Carathéodory distance (English)
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1990
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Für den Kreisring \(A:=\{\lambda \in {\mathbb{C}}:\) \(1/R<| \lambda | <R\}\) \((R>1)\) wird festgestellt, daß die Carathéodory Distanz \(C_ A\) keine innere Distanz ist. Mit einem einfachen Argument wird \(C_ A(1,-1)<C^ i_ A(1,-1)\) nachgewiesen. Hier bezeichne \(C^ i_ A\) die zu \(C_ A\) assoziierte innere Distanz. (In einer neuen Arbeit [Math. Ann. 289, 335-339 (1991)] geben die Autoren eine präzise Beschreibung der Paare \((z',z'')\in A\times A\) mit \(C_ A(z',z'')=C^ i_ A(z',z'').\))
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Carathéodory distance
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non-innerness
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annulus in \({\mathbb{C}}\)
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