In 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 isoperimetric filling functions. For a proper, cocompact, simply connected geodesic metric space of non-positive curvature in the sense of Alexandrov the asymptotic rank equals its Euclidean rank.
Cite this article
Stefan Wenger, The asymptotic rank of metric spaces. Comment. Math. Helv. 86 (2011), no. 2, pp. 247–275DOI 10.4171/CMH/223