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Sibirskii Matematicheskii Zhurnal, 2019, Volume 60, Number 2, Pages 391–400
DOI: https://doi.org/10.33048/smzh.2019.60.210 (Mi smj3082) 		 
This article is cited in 4 scientific papers (total in 4 papers)

Level sets of classes of mappings of two-step Carnot groups in a nonholonomic interpretation

M. B. Karmanova

Sobolev Institute of Mathematics, Novosibirsk, Russia
Full-text PDF (298 kB) Citations (4)
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DOI: https://doi.org/10.33048/smzh.2019.60.210
Abstract: We obtain the metric properties of level sets of certain sufficiently smooth mappings of two-step Carnot groups which are Hölder in the sub-Riemannian sense. In particular, we calculate the Hausdorff dimension of these sets and prove a coarea formula of a new type.
Keywords: two-step Carnot group, level set, Hausdorff dimension, coarea formula.
Funding agency Grant number
Russian Foundation for Basic Research 16-31-60036_мол_а_дк
The author was supported by the Russian Foundation for Basic Research (Grant 16-31-60036-mol-a-dk).
Received: 10.10.2017
Revised: 21.04.2018
English version:
Siberian Mathematical Journal, 2019, Volume 60, Issue 2, Pages 304–311
DOI: https://doi.org/10.1134/S0037446619020101
Bibliographic databases:
Document Type: Article
UDC: 514.7+517.4
Language: Russian
Citation: M. B. Karmanova, “Level sets of classes of mappings of two-step Carnot groups in a nonholonomic interpretation”, Sibirsk. Mat. Zh., 60:2 (2019), 391–400; Siberian Math. J., 60:2 (2019), 304–311
Citation in format AMSBIB
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    • This publication is cited in the following 4 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Сибирский математический журнал Siberian Mathematical Journal
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