On the strict concavity of the harmonic radius in dimension \(N\geqq 3\) (Q2765883)
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scientific article; zbMATH DE number 1695093
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On the strict concavity of the harmonic radius in dimension \(N\geqq 3\) |
scientific article; zbMATH DE number 1695093 |
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1 August 2002
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harmonic radius
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Robin function
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harmonic center
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0.9997785
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0.88691914
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0.8812233
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0.87706554
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On the strict concavity of the harmonic radius in dimension \(N\geqq 3\) (English)
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Let \(\Omega\) be a subset of \(\mathbb{R}^N\) and \(N\geq 3\). The authors prove the following results: NEWLINENEWLINENEWLINETheorem 1. Let \(\Omega\) be convex, then the harmonic radius of \(\Omega\) is a strictly convex function unless \(\Omega\) is a cylinder or a translate of a cone.NEWLINENEWLINENEWLINETheorem 2. Let \(\Omega\) be a bounded convex domain, then the Robin function is strictly convex and there is exactly one harmonic center.
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