The asymptotic rank of metric spaces

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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.
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

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Differential Geometry, Metric Geometry

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http://salesiana.dossiersoluciones.com/handle/123456789/171824

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/math/0701212
 http://arxiv.org/abs/math/0701212

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arXiv