Open AccessIsolated singularities of mappings with the inverse Poletsky inequality
Author(s) -
Evgeny Sevost’yanov
Publication year - 2021
Publication title -
matematičnì studìï/matematičnì studìï
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.482
H-Index - 8
eISSN - 2411-0620
pISSN - 1027-4634
DOI - 10.30970/ms.55.2.132-136
Subject(s) - mathematics , inverse , boundary (topology) , gravitational singularity , singularity , pure mathematics , exponent , image (mathematics) , function (biology) , euclidean geometry , inequality , combinatorics , mathematical analysis , discrete mathematics , geometry , computer science , philosophy , linguistics , artificial intelligence , evolutionary biology , biology
The manuscript is devoted to the study of mappingswith 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 reversePoletsky inequality include the classes of con\-for\-mal,quasiconformal, and quasiregular mappings. The subject of thisarticle is the question of removability an isolated singularity of amapping. The main result is as follows. Suppose that $f$ is an opendiscrete mapping between domains of a Euclidean $n$-dimensionalspace satisfying the inverse Poletsky inequality with someintegrable majorant $Q.$ If the cluster set of $f$ at some isolatedboundary point $x_0$ is a subset of the boundary of the image of thedomain, 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 H\"{o}lder continuous at $x_0$ withthe exponent $1/n.$