Skip to main content
SpringerLink
Log in

Coarea Formula for Functions on 2-Step Carnot Groups with Sub-Lorentzian Structure

  • MATHEMATICS
  • Published:
Doklady Mathematics Aims and scope Submit manuscript

Abstract

We consider C1-functions defined on two-step Carnot groups with a sub-Lorentzian structure defined by one horizontal direction with a negative squared length along it, and prove a nonholonomic coarea formula. A result of interest in itself concerns the correctness of the problem statement, namely, the level sets have to be spacelike.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

REFERENCES

  1. V. M. Miklyukov, A. A. Klyachin, and V. A. Klyachin. http://www.uchimsya.info/maxsurf.pdf

  2. V. N. Berestovskii and V. M. Gichev, St. Petersburg Math. J. 11 (4), 543–565 (2000).

    MathSciNet  Google Scholar 

  3. M. Grochowski, J. Dyn. Control Syst. 12 (2), 145–160 (2006).

    Google Scholar 

  4. A. Korolko and I. Markina, Complex Anal. Oper. Theory 4 (3), 589–618 (2010).

    Article  MathSciNet  Google Scholar 

  5. V. R. Krym and N. N Petrov, Vestn. St. Petersburg Univ. Math. 41 (3), 256–265 (2008).

    Article  Google Scholar 

  6. G. B. Folland and E. M. Stein, Hardy Spaces on Homogeneous Groups (Princeton Univ. Press, Princeton, 1982).

    MATH  Google Scholar 

  7. M. B. Karmanova, Sib. Math. J. 58 (2), 232–254 (2017).

    Article  MathSciNet  Google Scholar 

  8. P. Pansu, Ann. Math. 129, 1–60 (1989).

    Article  MathSciNet  Google Scholar 

  9. S. Vodopyanov, in The Interaction of Analysis and Geometry: Contemporary Mathematics (Am. Math. Soc., Providence, RI, 2007), Vol. 424, pp. 247–301.

  10. M. B. Karmanova, Dokl. Math. 95 (3), 199–202 (2017).

    Article  MathSciNet  Google Scholar 

  11. M. Karmanova and S. Vodopyanov, Acta Appl. Math. 128 (1), 67–111 (2013).

    Article  MathSciNet  Google Scholar 

  12. M. B. Karmanova, Izv. Math. 84 (1), 52–94 (2020).

    Article  Google Scholar 

Download references

Funding

This work was supported by the Mathematical Center in Akademgorodok under agreement no. 075-15-2019-1613 with the Ministry of Science and Higher Education of the Russian Federation.

Author information

Authors and Affiliations

  1. Sobolev Institute of Mathematics, Siberian Branch, Russian Academy of Sciences, 630090, Novosibirsk, Russia

    M. B. Karmanova

Authors
  1. M. B. Karmanova
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to M. B. Karmanova.

Additional information

Translated by I. Ruzanova

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Karmanova, M.B. Coarea Formula for Functions on 2-Step Carnot Groups with Sub-Lorentzian Structure. Dokl. Math. 101, 129–131 (2020). https://doi.org/10.1134/S1064562420020131

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1134/S1064562420020131

Keywords

Search

Navigation