Distinguishing properties of weak slice conditions. II (Q2879542)
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scientific article; zbMATH DE number 6018510
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Distinguishing properties of weak slice conditions. II |
scientific article; zbMATH DE number 6018510 |
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27 March 2012
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slice conditions
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quasihyperbolic metric
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math.MG
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math.FA
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0.97080445
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0.83137214
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0.80320144
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0.8000504
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Distinguishing properties of weak slice conditions. II (English)
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The authors consider weak slice domains. Their main result states that for each \(0<\alpha_0<1\), there are bounded domains \(\Omega_1\) and \(\Omega_2\) such thatNEWLINENEWLINE(a) \(\Omega_1\) is an \(\alpha\)-wslice domain if and only if \(0\leq \alpha\leq \alpha_0\), andNEWLINENEWLINE(b) \(\Omega_2\) is an \(\alpha\)-wslice domain if and only if \(\alpha_0\leq \alpha<1\).NEWLINENEWLINEThe authors also construct an example of a domain that is an \(\alpha\)-wslice domain exactly if \(\alpha\in [0,\alpha_0]\cup [\alpha_1,1)\).NEWLINENEWLINEFurther, an example is provided that is a \(0\)-wslice domain but not a slice domain.NEWLINENEWLINENEWLINEFor Part I see [the first and the third author, Conform. Geom. Dyn. 7, 49--75 (2003; Zbl 1064.30011)].
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