MATEMATIČKI VESNIK
МАТЕМАТИЧКИ ВЕСНИК



MATEMATIČKI VESNIK
A NOTE ON THE MINIMAL DISPLACEMENT FUNCTION
G. Bettencourt, S. Mendes

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.

Creative Commons License

Keywords: Minimal displacement function; metric space; subadditivity.

MSC: 51F99, 51K05

Pages:  297--302     

Volume  72 ,  Issue  4 ,  2020