On the Bloch constant (Q2758406)
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scientific article; zbMATH DE number 1679781
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On the Bloch constant |
scientific article; zbMATH DE number 1679781 |
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11 December 2002
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Bloch constant
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Bloch function
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0.91575044
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On the Bloch constant (English)
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The article presents a survey on Bloch constants for analytic, meromorphic and harmonic mappings of a single variable and several variables. Sections 1-5 are devoted to elementary concepts and results; Sections 6-8 deals with the Ahlfors lemma, the Julia lemma and related topics; Sections 9-10 are concerned with distortion theorems. In Sections 11-13 bounds of different Bloch constants are formulated. Section 14 deals with the ultrahyperbolic metric, Sections 15-17 are devoted to the Alhfors method to treat the spherical and hyperbolic Bloch constants. In Sections 18-19 the Bloch constants are introduced for harmonic mappings, quasiregular holomorphic mappings and Bloch mappings in several variables. Proofs of some theorems are given while some are only stated. A list of thirty nine relevant references is given. This survey article will be enormously helpful to a person interested to the theory of Bloch constants.NEWLINENEWLINEFor the entire collection see [Zbl 0972.00045].
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