Covering theorems on quasi-conformal mappings (Q2735376)
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scientific article; zbMATH DE number 1640373
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Covering theorems on quasi-conformal mappings |
scientific article; zbMATH DE number 1640373 |
Statements
6 November 2002
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covering theorems
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quasi-conformal mapping
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Covering theorems on quasi-conformal mappings (English)
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Let \(f(z)\) be a quasiconformal mapping of the unit disc \(\{z:|z|<1\}\) with \(f(0)=0\) satisfying \(\lim_{z\to 0}|f(z)|/ |z|^\beta= \alpha\) and NEWLINE\[NEWLINE\int^1_0 \bigl(\beta-1/\overline {D(r)}\bigr) dr/r\leq M.NEWLINE\]NEWLINE Then the image of \(f\) covers the disc \(\{w:|w|< (\alpha/4) e^{-M}\}\).
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