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Bettencourt, G. H. & Mendes, S. (2020). A note on the minimal displacement function. Matematicki Vesnik. 72 (4), 297-302
G. H. Bettencourt and S. M. Mendes, "A note on the minimal displacement function", in Matematicki Vesnik, vol. 72, no. 4, pp. 297-302, 2020
@article{bettencourt2020_1715096899894, author = "Bettencourt, G. H. and Mendes, S.", title = "A note on the minimal displacement function", journal = "Matematicki Vesnik", year = "2020", volume = "72", number = "4", pages = "297-302", url = "http://www.vesnik.math.rs/board.html" }
TY - JOUR TI - A note on the minimal displacement function T2 - Matematicki Vesnik VL - 72 IS - 4 AU - Bettencourt, G. H. AU - Mendes, S. PY - 2020 SP - 297-302 SN - 0025-5165 UR - http://www.vesnik.math.rs/board.html AB - Let (X,d) be a metric space and Iso(X,d) the associated isometry group. We study the subadditivity of the minimal displacement function $f : Iso(X, d) \to R$ for different metric spaces. When (X,d) is ultrametric, we prove that the minimal displacement function is subadditive. We show, by a simple algebraic argument, that subadditivity does not hold for the direct isometry group of the hyperbolic plane. The same argument can be used for other metric spaces. ER -