The asymptotic rank of metric spaces

• Autores: Stefan Wenger
• Localización: Commentarii mathematici helvetici, ISSN 0010-2571, Vol. 86, Nº 2, 2011, págs. 247-275
• Idioma: inglés
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• Resumen

  • 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.