Volume 221 (2018)
Isoperimetric characterization of upper curvature bounds
Pages: 159 – 202
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.
Received 9 December 2017
Published 6 November 2018