Isoperimetric inequalities of euclidean type in metric spaces

2003/06/05 by Stefan Wenger, Wenger, Stefan · 1 citation
Mathematics · #49Q15 #FOS: Mathematics #Functional Analysis (math.FA) #Geometric Analysis and Curvature Flows #Geometric and Algebraic Topology #Metric Geometry (math.MG) #Point processes and geometric inequalities #math.FA #math.MG #msc:49Q15

paper · pdf · doi:10.48550/arxiv.math/0306089

arxiv created 2003/06/05 · openalex publication_date 2003/06/05 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

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.

Citations

• Normal and Integral Currents

Cited by

• Isoperimetric inequalities in Hadamard spaces of asymptotic rank two

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