Geodesic
Sub-riemannian properties of the level sets of noncontact mappings of Heisenberg groups
Matematičeskie trudy, Tome 25 (2022) no. 2, pp. 107-125.

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

We consider a model example of noncontact mappings of Heisenberg groups where the dimension of the source space is greater than the dimension of the target space. We derive metric properties of level surfaces and prove an analog of the coarea formula. 
@article{MT_2022_25_2_a3,
     author = {M. B. Karmanova},
     title = {Sub-riemannian properties of the level sets of noncontact mappings of {Heisenberg} groups},
     journal = {Matemati\v{c}eskie trudy},
     pages = {107--125},
     publisher = {mathdoc},
     volume = {25},
     number = {2},
     year = {2022},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MT_2022_25_2_a3/}
}
TY  - JOUR
AU  - M. B. Karmanova
TI  - Sub-riemannian properties of the level sets of noncontact mappings of Heisenberg groups
JO  - Matematičeskie trudy
PY  - 2022
SP  - 107
EP  - 125
VL  - 25
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/MT_2022_25_2_a3/
LA  - ru
ID  - MT_2022_25_2_a3
ER  - 
%0 Journal Article
%A M. B. Karmanova
%T Sub-riemannian properties of the level sets of noncontact mappings of Heisenberg groups
%J Matematičeskie trudy
%D 2022
%P 107-125
%V 25
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/item/MT_2022_25_2_a3/
%G ru
%F MT_2022_25_2_a3
M. B. Karmanova. Sub-riemannian properties of the level sets of noncontact mappings of Heisenberg groups. Matematičeskie trudy, Tome 25 (2022) no. 2, pp. 107-125. http://geodesic.mathdoc.fr/item/MT_2022_25_2_a3/

[1] Franchi B., Serapioni R., and Serra Cassano F., “Rectifiability and perimeter in the Heisenberg group”, Math. Ann., 321:1 (1971), 479–531 | MR

[2] Basalaev S. G., “Odnomernye poverkhnosti urovnya $hc$-differentsiruemykh otobrazhenii prostranstv Karno — Karateodori”, Vestn. NGU, 13:4 (2013), 16–36 | Zbl

[3] Kozhevnikov A., Propriétés métriques des ensembles de niveau des applications différentiables sur les groupes de Carnot. Géométrie métrique, Université Paris Sud, Paris, 2015

[4] Franchi B., Serapioni R., “Intrinsic Lipschitz graphs within Carnot groups”, J. Geom. Anal.., 26:3 (2016), 1946–1994 | DOI | MR | Zbl

[5] Karmanova M., “O lokalnykh metricheskikh kharakteristikakh mnozhestv urovnya $C^1_H$-otobrazhenii mnogoobrazii Karno”, Sib. matem. zhurn., 60:6 (2019), 1291–1309 | MR | Zbl

[6] Karmanova M., “Mnozhestva urovnya klassov otobrazhenii dvustupenchatykh grupp Karno v negolonomnoi interpretatsii”, Sib. matem. zhurn., 60:2 (2019), 391–400 | MR | Zbl

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

[8] Pansu P., “Métriques de Carnot–Carathéodory et quasi-isométries des espaces symétriques de rang 1”, Math. Ann., 129:1 (1989), 1–60 | DOI | MR | Zbl

[9] Vodopyanov S., “Geometry of Carnot–Carathéodory Spaces and Differentiability of Mappings”, The Interaction of Analysis and Geometry, Contemporary Mathematics, 424, Amer. Math. Soc., Providence, RI, 2007, 247–301 | DOI | MR | Zbl

[10] Karmanova M., Vodopyanov S., “A Coarea Formula for Smooth Contact Mappings of Carnot–Caratheodory Spaces”, Acta Appl. Math., 128:1 (2013), 67–111 | DOI | MR | Zbl

[11] Karmanova M., “Sublorentseva formula koploschadi dlya otobrazhenii grupp Karno”, Sib. matem. zhurn., 63:3 (2022), 587–612 | Zbl

[12] Karmanova M., “Formula koploschadi na gruppakh Karno s sublorentsevoi strukturoi dlya vektor-funktsii”, Sib. matem. zhurn., 62:2 (2021), 298–325 | Zbl

[13] Federer H., Geometric Measure Theory, Springer, New York, 1969 | MR | Zbl

[14] Vodopyanov S. K., Ukhlov A. D., “Set functions and their applications in the theory of Lebesgue and Sobolev spaces. I”, Siberian Adv. Math., 14:4 (2004), 78–125 | MR | Zbl

[15] Vodopyanov S. K., Ukhlov A. D., “Set functions and their applications in the theory of Lebesgue and Sobolev spaces. II”, Siberian Adv. Math., 15:1 (2005), 91–125 | MR | Zbl

[16] Karmanova M., “Ploschad grafikov na proizvolnykh gruppakh Karno s sublorentsevoi strukturoi”, Sib. matem. zhurn., 61:4 (2020), 823–848 | MR | Zbl