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The Coarea Formula for Vector Functions on Carnot Groups with Sub-Lorentzian Structure

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Abstract

We establish the coarea formula as an expression for the measure of a subset of a Carnot group in terms of the sub-Lorentzian measure of the intersections of the subset with the level sets of a vector function. We describe the conditions for the level sets of vector functions to be spacelike and find the metric characteristics of these surfaces. Also, we address a series of relevant questions, in particular, about the uniqueness of the coarea factor.

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Funding

The author was supported by the Mathematical Center in Akademgorodok (Agreement No. 075–15–2019–1613 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, 2021, Vol. 62, No. 2, pp. 298–325. https://doi.org/10.33048/smzh.2021.62.205

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Karmanova, M.B. The Coarea Formula for Vector Functions on Carnot Groups with Sub-Lorentzian Structure. Sib Math J 62, 239–261 (2021). https://doi.org/10.1134/S0037446621020051

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  • DOI: https://doi.org/10.1134/S0037446621020051

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