Comparing hyperbolic distance with Kra's distance on the unit disk (Q436048)
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scientific article; zbMATH DE number 6060690
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Comparing hyperbolic distance with Kra's distance on the unit disk |
scientific article; zbMATH DE number 6060690 |
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Comparing hyperbolic distance with Kra's distance on the unit disk (English)
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28 July 2012
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Kra's distance
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hyperbolic distance
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quasiconformal mapping
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complete elliptic integral
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Kra's distance \(d_K\) is defined on a hyperbolic Riemann surface with the aid of Teichmüller's shift mappings. The author shows that for the unit disk \(\mathbb D\), NEWLINE\[NEWLINE 2d_K<d<\frac{\pi^2}{8}e^{d_K}, NEWLINE\]NEWLINE where \(d\) is the hyperbolic metric on \(\mathbb D\) and the constants are sharp. The proof uses an explicit expression for \(d_K\) on \(\mathbb D\) in terms of complete elliptic integrals.
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