Isolated singularities of mappings with the inverse Poletsky inequality - E.A. Sevost'yanov (Математичні Студії)
The manuscript is devoted to the study of mappings with finite distortion, which have been actively studied recently. We consider mappings satisfying the inverse Poletsky inequality, which can have branch points. Note that mappings with the reverse Poletsky inequality include the classes of con\-for\-mal, quasiconformal, and quasiregular mappings. The subject of this article is the question of removability an isolated singularity of a mapping. The main result is as follows. Suppose that $f$ is an open discrete mapping between domains of a Euclidean $n$-dimensional space satisfying the inverse Poletsky inequality with some integrable majorant $Q.$ If the cluster set of $f$ at some isolated boundary point $x_0$ is a subset of the boundary of the image of the domain, and, in addition, the function $Q$ is integrable, then $f$ has a continuous extension to $x_0.$ Moreover, if $f$ is finite at $x_0,$ then $f$ is logarithmic Hölder continuous at $x_0$ with the exponent $1/n.$