2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/171824In this article we define and study a notion of asymptotic rank for metric spaces and show in our main theorem that for a large class of spaces, the asymptotic rank is characterized by the growth of the higher filling functions. For a proper, cocompact, simply-connected geodesic metric space of non-curvature in the sense of Alexandrov the asymptotic rank equals its Euclidean rank.Theorem 4.1 in Version 2 and its proof have been moved into a new paper, see reference in the new version. Some new references have been addedDifferential GeometryMetric Geometrytext