Boundary behavior of derivatives of conformal mappings of simply connected domains (Q2018047)
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scientific article; zbMATH DE number 6418927
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Boundary behavior of derivatives of conformal mappings of simply connected domains |
scientific article; zbMATH DE number 6418927 |
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Boundary behavior of derivatives of conformal mappings of simply connected domains (English)
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24 March 2015
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Let \(G\) be a simply connected domain on the complex plane and \(\varphi(z)\) its conformal mapping onto the upper half-plane. Let \(\Gamma \subset\partial G\) be a smooth open Jordan arc reachable from inside of \(G\). Sufficient conditions for the existence of an angular limit of \(\varphi'(z)\) and its boundness at \(z \in \Gamma\) are found.
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conformal mapping
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angular limit of the derivative
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