Analogues of Sokhotski-Weierstrass and Picard theorems for mappings with finite length distortion (Q2901605)

The present article is devoted to the study of mappings with finite length distortion introduced by O. Martio, V. Ryazanov, U. Srebro and E. Yakubov in 2004. It is proved that isolated singularities are removable for open discrete mappings with finite length distortion provided that the inner dilatation has finite mean oscillation or logarithmic singularities of the order at most \(n-1\) on the corresponding set. As applications, analogues of the well-known Sokhotski-Weierstrass and Picard theorems are proved. In particular, it is shown that the mappings take any value in arbitrarily small neighborhoods of the essential singularity except, possibly, a set of capacity zero. The results of the work can be applied to various classes of spatial mappings with finite distortion.