The domains of admissible parameters of Box-quasimetrics of canonical Heisenberg groups and their generalizations
Matematičeskie trudy, Tome 27 (2024) no. 4, pp. 42-56 Cet article a éte moissonné depuis la source Math-Net.Ru

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For Heisenberg groups and some of their generalizations, geometric descriptions of the domains of admissible parameters $q_1,q_2$ for their $\mathrm{Box}$-quasimetrics considered as symmetric $(q_1,q_2)$ quasimetrics are obtained.
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A. V. Greshnov; S. A. Greshnova. The domains of admissible parameters of Box-quasimetrics of canonical Heisenberg groups and their generalizations. Matematičeskie trudy, Tome 27 (2024) no. 4, pp. 42-56. http://geodesic.mathdoc.fr/item/MT_2024_27_4_a3/

[1] Arutyunov A. V. and A. V. Greshnov A. V., “$(q_1,q_2)$-quasimetric spaces. Covering mappings and coincidence points”, Izvestiya: Mathematics, 82:2 (2018), 245–272 | DOI | DOI | MR

[2] Arutyunov A. V. and A. V. Greshnov A. V., “Theory of $(q_1, q_2)$-quasimetric spaces and coincidence points”, Dokl. Math., 94 (2016), 434-437 | DOI | DOI | MR

[3] Wilson W. A., “On quasi-metric spaces”, American J. of Math., 53 (1931), 675–684 | DOI | MR

[4] Arutyunov A. V. and Greshnov A. V., “$(q_1,q_2)$-quasimetric spaces. Covering mappings and coincidence points. A review of the results”, Fixed Point Theory, 23 (2022), 473-486 | DOI | MR

[5] Greshnov A. V., “$(q_1,q_2)$-quasimetrics bi-Lipschitz equivalent to 1-quasimetrics”, Siberian Adv. Math., 27 (2017), 253–262

[6] Vodopyanov S., “Geometry of Carnot–Carathéodory Spaes and Differentiability of Mappings”, Contemporary Mathematis, 424, AMS, Providene, RI, 2007, 247–301 | DOI | MR

[7] Karmanova M. and Vodop'yanov S., “Geometry of Carnot-Carathéodory spaces, differentiability, coarea and area formulas”, Analysis and Mathematical Physics, Trends Math., Birkhauser, Basel, 2009, 233–335 | MR

[8] Greshnov A. V., Tryamkin M. V., “Exact values of constants in the generalized triangle inequality for some $(1,q_2)$-quasimetrics on canonical Carnot groups”, Math. Notes. 2015, 98:4, 694–698 | DOI | MR

[9] Nagel A., Stein E. M. and Wainger S., “Balls and metrics defined by vector fields. I. Basic properties”, Acta Math., 155:1–2 (1985), 103–147 | DOI | MR

[10] Greshnov A. and Potapov V., “About coincidence points theorems on 2-step Carnot groups with 1-dimensional centre equipped with Box-quasimetrics”, AIMS Mathematics, 8:3 (2023), 6191–6205 | DOI | MR

[11] Greshnov A. V., “On finding the exact values of the constant in a $(1,q_2)$-generalized triangle inequality for Box-quasimetrics on 2-step Carnot groups with 1-dimensional center”, Sib. El. Math. Reports, 18:2 (2021), 1251–1260 | MR

[12] Ovsyannikov L. V., Group Analysis of Differential Equations, Academic, New York, 1982 | MR

[13] Postnikov M. M., Lectures in Geometry. Semester V: Lie Groups and Lie Algebras, Mir, M., 1982 | MR

[14] Agrachev A., Barilari D., Boscain U., A Comprehensive Introduction to sub-Riemannian Geometry, Camb. Univ. Press, Cambridge, 2020 | MR

[15] Bonfiglioli A., Lanconelli E., Uguzzoni F., Stratified Lie groups and potential theory for their sub-Laplacian, Springer-Verl., Berlin–Heidelberg, 2007 | MR