Continuously Removable Sets for Quasiconformal Mappings

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 → Rˉⁿ = 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. __________ Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 314, 2004, pp. 213–220.