Voir la notice de l'article provenant de la source Math-Net.Ru
@article{MT_2023_26_1_a4, author = {M. B. Karmanova}, title = {The area of surfaces on {sub-Lorentzian} structures of depth two}, journal = {Matemati\v{c}eskie trudy}, pages = {93--119}, publisher = {mathdoc}, volume = {26}, number = {1}, year = {2023}, language = {ru}, url = {http://geodesic.mathdoc.fr/item/MT_2023_26_1_a4/} }
M. B. Karmanova. The area of surfaces on sub-Lorentzian structures of depth two. Matematičeskie trudy, Tome 26 (2023) no. 1, pp. 93-119. http://geodesic.mathdoc.fr/item/MT_2023_26_1_a4/
[1] V. M. Miklyukov, A. A. Klyachin, V. A. Klyachin, Maksimalnye poverkhnosti v prostranstve-vremeni Minkovskogo, 2011 http://uchimsya.info/maxsurf.pdf
[2] G. L. Naher, The Geometry of Minkowski Spacetime. An Introduction to the Mathematics of the Special Theory of Relativity, Applied Mathematical Sciences, 92, Springer-Verlag, Berlin, 1992
[3] B. Nielsen, “Minimal immersion, Einstein's equations and Mach's principle”, J. Geom. Phys., 4 (1987), 1–20
[4] V. H. Berestovskii, V. M. Gichev, “Metrizovannye levoinvariantnye poryadki na topologicheskikh gruppakh”, Algebra i analiz, 11:4 (1999), 1–34
[5] M. Grochowski, “Reachable sets for the Heisenberg sub-Lorentzian structure on $\mathbb{R}^3$”, J. Dyn. Control Syst., 12:2 (2006), 145–160
[6] M. Grochowski, “Properties of reachable sets in the sub-Lorentzian geometry”, J. Geom. Phys., 59:7 (2009), 885–900
[7] M. Grochowski, “Normal forms and reachable sets for analytic Martinet sub-Lorentzian structures of Hamiltonian type”, J. Dyn. Control Syst., 17:1 (2011), 49–75
[8] M. Grochowski, “Reachable Sets For Contact sub-Lorentzian Metrics on R3”, J. Math. Sci., 177:3 (2011), 383–394
[9] M. Grochowski, “The structure of reachable sets for affine control systems induced by generalized Martinet sub-Lorentzian metrics”, ESAIM Control Optim. Calc. Var., 18:4 (2012), 1150–1177
[10] M. Grochowski, “The structure of reachable sets and geometric optimality of singular trajectories for certain affine control systems in R3. The sub-Lorentzian approach”, J. Dyn. Control Syst. (to appear)
[11] M. Grochowski, “Geodesies in the sub-Lorentzian geometry”, Bull. Pol. Acad. Sci. Math., 50:2 (2002), 161–178
[12] M. Grochowski, “Remarks on the global sub-Lorentzian geometry”, Anal. Math. Phys., 3:4 (2013), 295–309
[13] A. Korolko, I. Markina, “Lorentzian geometry on some H-type groups”, J. Geom. Anal., 19:4 (2009), 864–889
[14] A. Korolko, I. Markina, “Geodesies on H-type quaternion groups with sub-Lorentzian metric and their physical interpretation”, Complex Anal. Oper. Theory, 4:3 (2010), 589–618
[15] V. R. Krym, H. N. Petrov, “Uravneniya dvizheniya zaryazhennoi chastitsy v pyatimernoi modeli obschei teorii otnositelnosti s nego-lonomnym chetyrekhmernym prostranstvom skorostei”, Vestn. S-Peterb. un-ta. Ser. 1, 2007, no. 1, 62–70
[16] V. R. Krym, H. N. Petrov, “Tenzor krivizny i uravneniya Einshteina dlya chetyrekhmernogo negolonomnogo raspredeleniya”, Vestn. S-Peterb. un-ta. Ser. 1, 2008, no. 3, 68–80
[17] I. Bars, J. Terning, Extra dimensions in space and time, Springer, New York, 2010
[18] W. Craig, S. Weinstein, “On Determinism and Well-Posedness in Multiple Time Dimensions”, Proc. R. Soc. A, 465:2110 (2008), 3023–3046
[19] M. B. Karmanova, “Dvukhstupenchatye sublorentsevy struktury i poverkhnosti-grafiki”, Izv. RAN. Seriya Matematika, 84:1 (2020), 60–104
[20] M. B. Karmanova, “Ploschad grafikov na proizvolnykh gruppakh Karno s sublorentsevoi strukturoi”, Sib. matem. zhurn., 61:4 (2020), 823–848
[21] M. V. Karmanova, “Formula koploschadi na gruppakh Karno s sublorentsevoi strukturoi dlya vektor-funktsii”, Sib. matem. zhurn., 62:2 (2021), 298–325
[22] M. B. Karmanova, “Sublorentseva formula koploschadi dlya otobrazhenii grupp Karno”, Sib. matem. zhurn., 63:3 (2022), 587–612
[23] M. B. Karmanova, “Mera obrazov kontaktnykh otobrazhenii na dvukh-stupenchatykh sublorentsevykh strukturakh”, Matem. zametki, 113:1 (2023), 149–153
[24] G. B. Folland, E. M. Stein, Hardy spaces on homogeneous group, Princeton Univ. Press, Princeton, 1982
[25] M. B. Karmanova, “Ob approksimiruemosti i parametrizatsii proobrazov elementov grupp Karno na sublorentsevykh strukturakh”, Matem. zametki, 111:1 (2022), 140–144
[26] P. Pansu, “Metriques de Carnot-Caratheodory et quasi-isometries des espaces symetriques de rang 1”, Math. Ann., 129:1 (1982), 1–60
[27] S. Vodopyanov, “Geometry of Carnot-Caratheodory Spaces and Differentiability of Mappings”, Contemporary Mathematics, 424, AMS, Providence, RI, 2007, 247–301
[28] M. Karmanova, S. Vodopyanov, “An area formla for contact $C^1$-mappings of Carnot manifolds”, Complex Var. Elliptic Equ., 55:1–3 (2010), 317–329
[29] M. B. Karmanova, “Formula ploschadi dlya lipshitsevykh otobrazhenii prostranstv Karno–Karateodori”, Izv. RAN. Ser. mat., 78:3 (2014), 53–78