Isoperimetric inequalities of euclidean type in metric spaces

Mathematics – Functional Analysis

Scientific paper

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Scientific paper

In this paper we prove an isoperimetric inequality of euclidean type for
complete metric spaces admitting a cone-type inequality. These include all
Banach spaces and all complete, simply-connected metric spaces of non-positive
curvature in the sense of Alexandrov or, more generally, of Busemann. The main
theorem generalizes results of Gromov and Ambrosio-Kirchheim.

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