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Continuously Removable Sets for Quasiconformal Mappings

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Abstract

Let D be a domain in the n-dimensional Euclidean space Rn, n ≥ 2, and let E be a compact in D. The paper presents conditions on the compact E under which any homeomorphic mapping f = D ∖ E → Rn can be extended to a continuous mapping f = D → R¯n = Rn ⋃ {∞}. These conditions define the class of NCS-compacts, which, for n = 2, coincides with the class of topologically removable compacts for conformal and quasiconformal mappings. Bibliography: 11 titles.

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Authors and Affiliations

  1. Far-Eastern State University, Vladivostock, Russia

    A. V. Tyutyuev & V. A. Shlyk

Authors
  1. A. V. Tyutyuev
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  2. V. A. Shlyk
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Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 314, 2004, pp. 213–220.

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Tyutyuev, A.V., Shlyk, V.A. Continuously Removable Sets for Quasiconformal Mappings. J Math Sci 133, 1728–1732 (2006). https://doi.org/10.1007/s10958-006-0084-z

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