On some properties of generalized quasiisometries with unbounded characteristic - Sevost'yanov, E. A. (Ukrains’kyi Matematychnyi Zhurnal, 2011)
We consider a family of the open discrete mappings f: D → R^n that distort in a special way the p -modulus of families of curves connecting the components of spherical condenser in a domain D in R^n, p > n — 1, p < n, and omitting a set of positive p-capacity. We establish that this family is normal provided that some function realizing the control of the considered distortion of curve family has a finite mean oscillation at every point or only logarithmic singularities of the order, which is not larger than n − 1. We prove that, under these conditions, an isolated singularity x_0 D of the mapping f : D {x_0} → R^n is removable and, moreover, the extended mapping is open and discrete. As applications we obtain analogs of the known Liouville and Sokhotski – Weierstrass theorems.