On Removable Singularities of Maps with Growth Bounded by a Function

E. A. Sevost'yanov

Zhytomyr I. Franko State University

Abstract: This paper studies questions related to the local behavior of almost everywhere differentiable maps with the $N$, $N^{-1}$, $ACP$, and $ACP^{-1}$ properties whose quasiconformality characteristic satisfies certain growth conditions. It is shown that, if a map of this type grows in a neighborhood of an isolated boundary point no faster than a function of the radius of a ball, then this point is either a removable singular point or a pole of this map.

Keywords: removable singularity, essential singularity, pole, function of bounded growth, Luzin's properties $N$ and $N^{-1}$, class $ACP$, class $ACP^{-1}$.

UDC: 517.5

Received: 22.12.2012
Revised: 06.06.2014

DOI: 10.4213/mzm10406

 English version: Mathematical Notes, 2015, 97:3, 438–449

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