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.
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Funding
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.
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Translated from Sibirskii Matematicheskii Zhurnal, 2024, Vol. 65, No. 1, pp. 57–73. https://doi.org/10.33048/smzh.2024.65.106
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Isangulova, D.V. Topological Properties of Mappings with Finite Distortion on Carnot Groups. Sib Math J 65, 48–61 (2024). https://doi.org/10.1134/S0037446624010063
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DOI: https://doi.org/10.1134/S0037446624010063