The asymptotic rank of metric spaces

Stefan Wenger

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arXiv · math/0701212

The asymptotic rank of metric spaces

Stefan Wenger

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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.

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Stefan Wenger. 2008-10-20. The asymptotic rank of metric spaces. https://arxiv.org/abs/math/0701212

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