Journal of Mathematical Sciences

, Volume 133, Issue 6, pp 1728–1732 | Cite as

Continuously Removable Sets for Quasiconformal Mappings

  • A. V. Tyutyuev
  • V. A. Shlyk


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.


Continuous Mapping Euclidean Space Quasiconformal Mapping Homeomorphic Mapping 
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Copyright information

© Springer Science+Business Media, Inc. 2006

Authors and Affiliations

  • A. V. Tyutyuev
    • 1
  • V. A. Shlyk
    • 1
  1. 1.Far-Eastern State UniversityVladivostockRussia

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