Abstract
Necessary maximality conditions for graph surfaces in a class of two-step sub-Lorentzian structures are obtained. The concept of a sub-Lorentzian mean curvature is introduced, and equations for maximal surfaces are deduced.
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V. M. Miklyukov, A. A. Klyachin, and V. A. Klyachin, http://www.uchimsya.info/maxsurf.pdf.
V. N. Berestovskii and V. M. Gichev, St. Petersb. Math. J. 11 (4), 543–565 (2000).
M. Grochowski, J. Dyn. Control Syst. 12 (2), 145–160 (2006).
V. R. Krym and N. N. Petrov, Vestn. S.-Peterb. Univ., Ser. 1., No. 3, 68–80 (2008).
W. Craig and S. Weinstein, Proc. R. Soc. A 465 (2110), 3023–3046 (2008).
I. Bars and J. Terning, Extra Dimensions in Space and Time (Springer, Berlin, 2010).
M. B. Karmanova, Dokl. Math. 95 (3), 199–202 (2017).
M. B. Karmanova, Dokl. Math. 93 (3), 276–279 (2016).
G. B. Folland and E. M. Stein, Hardy Spaces on Homogeneous Groups (Princeton Univ. Press, Princeton, 1982).
S. Vodopyanov, The Interaction of Analysis and Geometry: Contemporary Mathematics (Am. Math. Soc., Providence, RI, 2007), pp. 247–301.
M. B. Karmanova, Sib. Math. J. 58 (2), 232–254 (2017).
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Original Russian Text © M.B. Karmanova, 2018, published in Doklady Akademii Nauk, 2018, Vol. 480, No. 1, pp. 16–20.
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Karmanova, M.B. Class of Maximal Graph Surfaces on Multidimensional Two-Step Sub-Lorentzian Structures. Dokl. Math. 97, 207–210 (2018). https://doi.org/10.1134/S1064562418030043
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DOI: https://doi.org/10.1134/S1064562418030043