On quasimöbius maps in real Banach spaces (Q375522)
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scientific article; zbMATH DE number 6221333
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On quasimöbius maps in real Banach spaces |
scientific article; zbMATH DE number 6221333 |
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On quasimöbius maps in real Banach spaces (English)
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31 October 2013
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The authors give a sufficient (and necessary) condition for the image of a uniform domain to be a uniform domain under a coarsely quasihyperbolic homeomorphism. They thus answer in the affirmative a question raised by \textit{J. Väisälä} [``Free quasiconformality in Banach spaces. II'', Ann. Acad. Sci. Fenn., Ser. A I, Math. 16, No. 2, 255--310 (1991; Zbl 0761.30014)], where he proved the necessity of the condition. The condition is in terms of extending a coarsely quasihyperbolic homeomorphism to the closure of the domain in a controlled way.
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quasimöbius maps
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uniform domains
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coarsely quasihyperbolic
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