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September 2018 Isoperimetric characterization of upper curvature bounds
Alexander Lytchak, Stefan Wenger
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Acta Math. 221(1): 159-202 (September 2018). DOI: 10.4310/ACTA.2018.v221.n1.a5

Abstract

We prove that a proper geodesic metric space has non-positive curvature in the sense of Alexandrov if and only if it satisfies the Euclidean isoperimetric inequality for curves. Our result extends to non-geodesic spaces and non-zero curvature bounds.

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Alexander Lytchak. Stefan Wenger. "Isoperimetric characterization of upper curvature bounds." Acta Math. 221 (1) 159 - 202, September 2018. https://doi.org/10.4310/ACTA.2018.v221.n1.a5

Information

Received: 9 December 2017; Published: September 2018
First available in Project Euclid: 19 June 2019

zbMATH: 06983627
MathSciNet: MR3877021
Digital Object Identifier: 10.4310/ACTA.2018.v221.n1.a5

Rights: Copyright © 2018 Institut Mittag-Leffler

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Vol.221 • No. 1 • September 2018
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