Isometric actions on locally compact finite rank median spaces
Lamine Messaci
Université Côte d’Azur, Nice, France

Abstract
We prove that a connected locally compact median space of finite rank which admits a transitive action is isometric to endowed with the -metric. On the other hand, replacing the transitivity assumption on the group of isometries by a certain regularity of the action on the compactification of the space, we show that all orbits are discrete. In the course of proving these results, we provide a characterization of compactness in complete median spaces of finite rank by the combinatorics of their halfspaces.
Cite this article
Lamine Messaci, Isometric actions on locally compact finite rank median spaces. Groups Geom. Dyn. (2025), published online first
DOI 10.4171/GGD/868