Geodesic
Minimal graph-surfaces on arbitrary two-step Carnot groups
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 5 (2019), pp. 15-29.

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We establish basic properties of minimal graph-surfaces constructed from classes of mappings defined on two-step Carnot groups. Research methods include solving of a specific question on correctness of the problem statement. A main result on necessary minimality conditions is formulated in terms of sub-Riemannian analog of mean curvature.
Keywords: two-step Carnot group, graph-mapping, minimal surface, mean curvature. 
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M. B. Karmanova. Minimal graph-surfaces on arbitrary two-step Carnot groups. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 5 (2019), pp. 15-29. http://geodesic.mathdoc.fr/item/IVM_2019_5_a1/

[1] Karmanova M., Vodopyanov S., “Geometry of Carnot–Carathéodory spaces, differentiability, coarea and area formulas”, Anal. and Math. Phys., Birkhäuser, Basel, 2009, 233–335 | DOI | MR | Zbl

[2] Karmanova M. B., “Variatsii otobrazhenii s negolonomnym obrazom i primeneniya k teorii maksimalnykh poverkhnostei”, Dokl. RAN, 468:3 (2016), 257–260 | DOI | MR | Zbl

[3] Karmanova M. B., “Maksimalnye poverkhnosti na pyatimernykh gruppovykh strukturakh”, Sib. matem. zhurn., 59:3 (2018), 561–579 | MR | Zbl

[4] Karmanova M. B., “Grafiki lipshitsevykh funktsii i minimalnye poverkhnosti na gruppakh Karno”, Sib. matem. zhurn., 53:4 (2012), 839–861 | MR | Zbl

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

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

[7] Vodopyanov S., “Geometry of Carnot–Carathéodory spaces and differentiablity of mappings”, The Interaction Anal. and Geometry, Contemp. Math., 424, Amer. Math. Soc., Providence, RI, 2007, 247–301 | DOI | MR | Zbl

[8] Karmanova M. B., “O polinomialnoi subrimanovoi differentsiruemosti nekotorykh gëlderovykh otobrazhenii grupp Karno”, Sib. matem. zhurn., 58:2 (2017), 305–332 | MR | Zbl

[9] Karmanova M. B., “Formuly ploschadi dlya klassov gëlderovykh otobrazhenii grupp Karno”, Sib. matem. zhurn., 58:5 (2017), 1056–1079 | MR | Zbl