The asymptotic rank of metric spaces
Differential Geometry
2008-10-20 v3 Metric Geometry
Abstract
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 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.
Keywords
Cite
@article{arxiv.math/0701212,
title = {The asymptotic rank of metric spaces},
author = {Stefan Wenger},
journal= {arXiv preprint arXiv:math/0701212},
year = {2008}
}
Comments
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 added