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Sibirskii Matematicheskii Zhurnal, 2024, Volume 65, Number 1, Pages 57–73
DOI: https://doi.org/10.33048/smzh.2024.65.106 (Mi smj7840) 		 
Topological properties of mappings with finite distortion on Carnot groups

D. V. Isangulova

Novosibirsk State University
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DOI: https://doi.org/10.33048/smzh.2024.65.106
Abstract: We prove that every mapping with finite distortion on a Carnot group is open and discrete provided that it is quasilight and the distortion coefficient is integrable. Also, we estimate the Hausdorff dimension of the preimages of points for mappings on a Carnot group with a bounded multiplicity function and summable distortion coefficient. Furthermore, we give some example showing that the obtained estimates cannot be improved.
Keywords: Carnot group, mapping with finite distortion, quasilightness, openness, discreteness.
Funding agency Grant number
Ministry of Science and Higher Education of the Russian Federation 075-15-2022-282
The work is supported by the Mathematical Center in Akademgorodok under Agreement 075–15–2022–282 with the Ministry of Science and Higher Education of the Russian Federation.
Received: 14.09.2023
Revised: 18.10.2023
Accepted: 28.11.2023
English version:
Siberian Mathematical Journal, 2024, Volume 65, Issue 1, Pages 48–61
DOI: https://doi.org/10.1134/S0037446624010063
Document Type: Article
UDC: 517.54
MSC: 35R30
Language: Russian
Citation: D. V. Isangulova, “Topological properties of mappings with finite distortion on Carnot groups”, Sibirsk. Mat. Zh., 65:1 (2024), 57–73; Siberian Math. J., 65:1 (2024), 48–61
Citation in format AMSBIB
\Bibitem{Isa24}
\by D.~V.~Isangulova
\paper Topological properties of mappings with finite distortion on Carnot groups
\jour Sibirsk. Mat. Zh.
\yr 2024
\vol 65
\issue 1
\pages 57--73
\mathnet{http://mi.mathnet.ru/smj7840}
\transl
\jour Siberian Math. J.
\yr 2024
\vol 65
\issue 1
\pages 48--61
\crossref{https://doi.org/10.1134/S0037446624010063}
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