2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/229099The main purpose of the paper is to find some expansion properties of locally finite metric spaces which do not embed coarsely into a Hilbert space. The obtained result is used to show that infinite locally finite graphs excluding a minor embed coarsely into a Hilbert space. In an appendix a direct proof of the latter result is given.Some misprints have been corrected in the second versionMetric GeometryFunctional Analysis46B20; 05C12; 54E35Expansion properties of metric spaces not admitting a coarse embedding into a Hilbert spacetext