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http://hdl.handle.net/10071/21305
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Title: A note on the minimal displacement function
Authors: Bettencourt, G. H.
Mendes, S.
Keywords: Minimal displacement function
Metric space
Subadditivity
Issue Date: 2020
Publisher: Društvo matematičara Srbije
Abstract: 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.
Peer reviewed: yes
URI: http://hdl.handle.net/10071/21305
ISSN: 2406-0682
Ciência-IUL: https://ciencia.iscte-iul.pt/id/ci-pub-78270
Appears in Collections:DM-RI - Artigos em revistas científicas internacionais

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