Abstract
It is shown that the Hausdorff―Gromov distance between the discrete Heisenberg group Γ with a word metric and the asymptotic cone of Γ is finite. Bibliography: 8 titles.
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REFERENCES
D. Burago, “Periodic metrics” Advances Sov. Math., 9, 241-248 (1992).
S. V. Buyalo, Introduction to Metric Geometry [in Russian], Obrazovanie, St. Petersburg (1997).
M. Gromov, “Carnot-Carathéodory spaces seen from within” IHES/M/94/6.
M. Gromov, “Asymptotic invariants of infinite groups” in: G. A. Noble and M. A. Roller (eds.), Geometric Group Theory, Vol. 2, (London Math. Soc. Lect. Notes Ser., 182), Cambridge Univ. Press, Cambridge (1993).
M. Gromov, Structures Metriques pour les Varietes Riemanniennes, redige par J. Lafontaine en P. Pansu, Cedic/Fernand Nathan (1981).
K. Leichtweiss, Konvexe Mengen, Springer-Verlag, Berlin (1980).
P. Pansu, “Croissance des boules et des géodésiques fermées dans les nilvariétés” Ergod. Th. Dynam. Sys., 3, 415-445 (1983).
V. N. Berestovskii, “Geodesics of nonholonomic left-invariant inner metrics on the Heisenberg group and isoperimetrices of the Minkowski plane” Sib. Mat. Zh., 35, No. 1 (1994).
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Krat, S.A. Asymptotic Properties of the Heisenberg Group. Journal of Mathematical Sciences 110, 2824–2840 (2002). https://doi.org/10.1023/A:1015306413677
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DOI: https://doi.org/10.1023/A:1015306413677