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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 $ACP^{-1}$.
Received: 22.12.2012 Revised: 06.06.2014
Citation:
E. A. Sevost'yanov, “On Removable Singularities of Maps with Growth Bounded by a Function”, Mat. Zametki, 97:3 (2015), 448–461; Math. Notes, 97:3 (2015), 438–449
Linking options:
https://www.mathnet.ru/eng/mzm10406https://doi.org/10.4213/mzm10406 https://www.mathnet.ru/eng/mzm/v97/i3/p448
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Abstract page: | 314 | Full-text PDF : | 140 | References: | 60 | First page: | 15 |
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