Isoperimetric characterization of upper curvature bounds
classification
🧮 math.DG
math.MG
keywords
curvatureboundsisoperimetricalexandrovcharacterizationcurveseuclideanextends
read the original 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.
This paper has not been read by Pith yet.
discussion (0)
Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.