Geodesic
On~the removal of singularities of quasiconformal mappings
Sbornik. Mathematics, Tome 21 (1973) no. 2, pp. 240-254

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In this paper some questions concerning the removal of singular sets for quasiconformal mappings are considered. Unlike previously existing results, in which it was required that the mapping be a homeomorphism or that the capacity of the singular points be zero, in this paper the restriction is weaker: the Hausdorff measure of the singular points is less than $n-1$. A series of examples is given which show how to construct a set of singular points. In addition, theorems on removable singular sets are proved in which the quasiconformal mapping always has a continuous extension. In particular, the principle of symmetry for quasiconformal mappings is proved. Bibliography: 16 titles. 
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     author = {E. A. Poletskii},
     title = {On~the removal of singularities of quasiconformal mappings},
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E. A. Poletskii. On~the removal of singularities of quasiconformal mappings. Sbornik. Mathematics, Tome 21 (1973) no. 2, pp. 240-254. http://geodesic.mathdoc.fr/item/SM_1973_21_2_a4/