Bi-Lipschitz extensions in the plane (Q1909252)
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scientific article; zbMATH DE number 854438
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Bi-Lipschitz extensions in the plane |
scientific article; zbMATH DE number 854438 |
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Bi-Lipschitz extensions in the plane (English)
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24 February 1999
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\textit{P. Tukia} [Ann. Acad. Sci. Fenn., Ser. A I, Math. 5, 49-72 (1980; Zbl 0411.57015] showed that any bi-Lipschitz map of a circle, a line, or an interval into the plane with a bi-Lipschitz constant \(M\) has an extension to a bi-Lipschitz map of the plane onto itself with the bi-Lipschitz constant depending only on \(M\). In the present paper the author extends this theorem to bi-Lipschitz maps of arbitrary subsets of a line or a circle.
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bi-Lipschitz map
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planar Schoenflies theorem
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extension
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