Abstract:
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.
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