The asymptotic rank of metric spaces

Details The asymptotic rank of metric spaces The asymptotic rank of metric spaces

2007-01-08

arxiv.org/abs/math/0701212v3

Mathematics

Differential Geometry

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

Scientific paper

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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