Isoperimetric characterization of upper curvature bounds

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.

References in corpus (3)

• Filling minimality of Finslerian 2-discs
• Intrinsic isometries in Euclidean space
• The intrinsic geometry of a Jordan domain

Cited by in corpus (1)

• Majorization by Hemispheres & Quadratic Isoperimetric Constants