Acta Mathematica

Isoperimetric characterization of upper curvature bounds

Alexander Lytchak and Stefan Wenger

Full-text: Open access

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.

Article information

Source
Acta Math., Volume 221, Number 1 (2018), 159-202.

Dates
Received: 9 December 2017
First available in Project Euclid: 19 June 2019

Permanent link to this document
https://projecteuclid.org/euclid.acta/1560966804

Digital Object Identifier
doi:10.4310/ACTA.2018.v221.n1.a5

Mathematical Reviews number (MathSciNet)
MR3877021

Zentralblatt MATH identifier
06983627

Citation

Lytchak, Alexander; Wenger, Stefan. Isoperimetric characterization of upper curvature bounds. Acta Math. 221 (2018), no. 1, 159--202. doi:10.4310/ACTA.2018.v221.n1.a5. https://projecteuclid.org/euclid.acta/1560966804


Export citation