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Sub-Lorentzian Coarea Formula for Mappings of Carnot Groups

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Abstract

Considering the class of contact mappings of Carnot groups with a multidimensional sub-Lorentzian structure on the preimages, we prove that the tangent plane approximates the level sets to a higher order than in the classical case. We also obtain a coarea formula for such mappings with a sub-Lorentzian measure on the level sets.

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Funding

The author was supported by the Mathematical Center in Akademgorodok under Agreement 075–15–2022–281 on 05.04.2022 with the Ministry of Science and Higher Education of the Russian Federation.

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Authors and Affiliations

  1. Sobolev Institute of Mathematics, Novosibirsk, Russia

    M. B. Karmanova

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  1. M. B. Karmanova
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Correspondence to M. B. Karmanova.

Additional information

Translated from Sibirskii Matematicheskii Zhurnal, 2022, Vol. 63, No. 3, pp. 587–612. https://doi.org/10.33048/smzh.2022.63.309

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Karmanova, M.B. Sub-Lorentzian Coarea Formula for Mappings of Carnot Groups. Sib Math J 63, 485–508 (2022). https://doi.org/10.1134/S0037446622030090

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  • DOI: https://doi.org/10.1134/S0037446622030090

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