Geodesic
Space-likeness of classes of level surfaces on Carnot groups and their metric properties
Doklady Rossijskoj akademii nauk. Matematika, informatika, processy upravleniâ, Tome 492 (2020), pp. 38-42.

Voir la notice de l'article provenant de la source Math-Net.Ru

We consider $C^1$-smooth vector functions defined on Carnot groups of arbitrary depth, deduce conditions for space-likeness of their level surfaces, and describe their metric properties from the viewpoint of sub-Lorentzian geometry. We prove the coarea formula as an expression of the measure of a subset of a Carnot group in terms of the sub-Lorentzian measures of its intersections with level sets of a vector function.
Keywords: Carnot group, sub-Lorentzian structure, vector function, level set, sub-Lorentzian measure, coarea formula. 
@article{DANMA_2020_492_a7,
     author = {M. B. Karmanova},
     title = {Space-likeness of classes of level surfaces on {Carnot} groups and their metric properties},
     journal = {Doklady Rossijskoj akademii nauk. Matematika, informatika, processy upravleni\^a},
     pages = {38--42},
     publisher = {mathdoc},
     volume = {492},
     year = {2020},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/DANMA_2020_492_a7/}
}
TY  - JOUR
AU  - M. B. Karmanova
TI  - Space-likeness of classes of level surfaces on Carnot groups and their metric properties
JO  - Doklady Rossijskoj akademii nauk. Matematika, informatika, processy upravleniâ
PY  - 2020
SP  - 38
EP  - 42
VL  - 492
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/DANMA_2020_492_a7/
LA  - ru
ID  - DANMA_2020_492_a7
ER  - 
%0 Journal Article
%A M. B. Karmanova
%T Space-likeness of classes of level surfaces on Carnot groups and their metric properties
%J Doklady Rossijskoj akademii nauk. Matematika, informatika, processy upravleniâ
%D 2020
%P 38-42
%V 492
%I mathdoc
%U http://geodesic.mathdoc.fr/item/DANMA_2020_492_a7/
%G ru
%F DANMA_2020_492_a7
M. B. Karmanova. Space-likeness of classes of level surfaces on Carnot groups and their metric properties. Doklady Rossijskoj akademii nauk. Matematika, informatika, processy upravleniâ, Tome 492 (2020), pp. 38-42. http://geodesic.mathdoc.fr/item/DANMA_2020_492_a7/

[1] Karmanova M.B., “Formula koploschadi dlya funktsii na 2-stupenchatykh gruppakh Karno s sublorentsevoi strukturoi”, DAN, 490 (2020), 42–46 | Zbl

[2] Miklyukov V.M., Klyachin A.A., Klyachin V.A., Maksimalnye poverkhnosti v prostranstve-vremeni Minkovskogo http://www.uchimsya.info/maxsurf.pdf

[3] Berestovskii V.N., Gichev V.M., Algebra i analiz, 11:4 (1999), 1–34 | MR | Zbl

[4] Grochowski M., J. Dyn. Control Syst., 12:2 (2006), 145–160 | DOI | MR | Zbl

[5] Korolko A., Markina I., Complex Anal. Oper. Theory, 4:3 (2010), 589–618 | DOI | MR | Zbl

[6] Krym V.R., Petrov N.N., Vestn. S.-Peterb. un-ta. Ser. 1, 2008, no. 3, 68–80 | Zbl

[7] Folland G.B., Stein, E.M., Hardy spaces on homogeneous groups, Princeton Univ. Press, Princeton, 1982 | MR | Zbl

[8] Karmanova M.B., Sib. mat. zhurn., 58:2 (2017), 232–254 | MR | Zbl

[9] Pansu P., Ann. Math., 129 (1989), 1–60 | DOI | MR | Zbl

[10] Vodopyanov S., Contemporary Mathematics, 424, Amer. Math. Soc., Providence, RI, 2007, 247–301 | DOI | MR | Zbl

[11] Karmanova M.B., DAN, 474:2 (2017), 151–154 | Zbl

[12] Karmanova M.B., Izv. RAN. Ser. mat., 84:1 (2020), 60–104 | DOI | MR | Zbl

[13] Karmanova M., Vodopyanov S., Acta Applicandae Mathematicae, 128:1 (2013), 67–111 | DOI | MR | Zbl

[14] Gromov M., Sub-Riemannian Geometry, Birkhäuser Verlag, Basel, 1996, 79–318 | DOI

[15] Basalaev S.G., Vodopyanov S.K., Euras. Math. J., 4:2 (2013), 10–48 | MR | Zbl