The asymptotic rank of metric spaces

Wenger, Stefan

doi:10.4171/CMH/223

Commentarii Mathematici Helvetici

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Volume 86, Issue 2, 2011, pp. 247–275

DOI: 10.4171/CMH/223

Published online: 2011-02-27

The asymptotic rank of metric spaces

Stefan Wenger^[1]

(1) University of Illinois at Chicago, USA

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.

Keywords: Isoperimetric inequalities, asymptotic rank, Euclidean rank, non-positive curvature, Hadamard spaces, cone type inequalities

Wenger Stefan: The asymptotic rank of metric spaces. Comment. Math. Helv. 86 (2011), 247-275. doi: 10.4171/CMH/223