On some properties of generalized quasiisometries with unbounded characteristic

We consider a family of open discrete mappings f:D ?[`(mathbb R<sup>n</sup>)] f:D to overline {{{mathbb R}^n}} that distort, in a special way, the p-modulus of a family of curves that connect the plates of a spherical condenser in a domain D in mathbb R<sup>n</sup> {{mathbb R}^n} ; p > n-1; p < n; and bypass a set of positive p-capacity. We establish that this family is normal if a certain real-valued function that controls the considered distortion of the family of curves has finite mean oscillation at every point or only logarithmic singularities of order not higher than n - 1: We show that, under these conditions, an isolated singularity x <sub>0</sub> ∈ D of a mapping f:D{ x<sub>0</sub> } ?[`(mathbb Rⁿ)] f:Dbackslash left{ {{x_0}} right} to overline {{{mathbb R}^n}} is removable, and, moreover, the extended mapping is open and discrete. As applications, we obtain analogs of the known Liouville and Sokhotskii–Weierstrass theorems.