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This article is cited in 9 scientific papers (total in 9 papers)
Area formulas for classes of Hölder continuous mappings of Carnot groups
M. B. Karmanova
Sobolev Institute of Mathematics, Novosibirsk, Russia
Abstract:
We prove area formulas for classes of the mappings that are Hölder continuous in the sub-Riemannian sense and defined on nilpotent graded groups. Moreover, in one of the model cases, we establish an area formula for calculating the initial measure and a measure close to it.
Keywords:
nilpotent graded group, Carnot group, Hölder continuous mapping, Lipschitz continuous mapping, graph mapping, intrinsic measure, area 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). |
DOI:
https://doi.org/10.17377/smzh.2017.58.509
 Full text:
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English version:
Siberian Mathematical Journal, 2017, 58:5, 817–836
Bibliographic databases:
  
UDC:
517.3+514.7
MSC: 35R30
Received: 10.11.2016
Citation:
M. B. Karmanova, “Area formulas for classes of Hölder continuous mappings of Carnot groups”, Sibirsk. Mat. Zh., 58:5 (2017), 1056–1079; Siberian Math. J., 58:5 (2017), 817–836
Citation in format AMSBIB
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Linking options:
http://mi.mathnet.ru/eng/smj2919 http://mi.mathnet.ru/eng/smj/v58/i5/p1056
Citing articles on Google Scholar:
Russian citations,
English citations
Related articles on Google Scholar:
Russian articles,
English articles
This publication is cited in the following articles:
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M. B. Karmanova, “Polynomial sub-Riemannian differentiability on Carnot–Carathéodory spaces”, Siberian Math. J., 59:5 (2018), 860–869
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M. B. Karmanova, “Metric properties of level surfaces of Hölder mappings defined on two-step Carnot groups”, Dokl. Math., 97:2 (2018), 122–124
  -
M. B. Karmanova, “Level sets of classes of mappings of two-step Carnot groups in a nonholonomic interpretation”, Siberian Math. J., 60:2 (2019), 304–311
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M. B. Karmanova, “Minimalnye poverkhnosti-grafiki na proizvolnykh dvustupenchatykh gruppakh Karno”, Izv. vuzov. Matem., 2019, no. 5, 15–29
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M. B. Karmanova, “On the class of Hölder surfaces in Carnot–Carathéodory spaces”, Siberian Math. J., 60:5 (2019), 861–885
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M. B. Karmanova, “O lokalnykh metricheskikh kharakteristikakh mnozhestv urovnya $C^1_H$-otobrazhenii mnogoobrazii Karno”, Sib. matem. zhurn., 60:6 (2019), 1291–1309
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M. B. Karmanova, “Two-step sub-Lorentzian structures and graph surfaces”, Izv. Math., 84:1 (2020), 52–94
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M. B. Karmanova, “A Metric Characteristic of Minimal Surfaces on Arbitrary Carnot Groups”, Math. Notes, 108:6 (2020), 895–900
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M. B. Karmanova, “Klassy maksimalnykh poverkhnostei na gruppakh Karno”, Sib. matem. zhurn., 61:5 (2020), 1009–1026
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