Isoperimetric characterization of upper curvature bounds

Alexander Lytchak Universit¨at K¨oln Stefan Wenger University of Fribourg

Metric Geometry mathscidoc:1911.43028

Acta Mathematica, 221, (1), 159 – 202, 2018
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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  title={Isoperimetric characterization of upper curvature bounds},
  author={Alexander Lytchak, and Stefan Wenger},
  booktitle={Acta Mathematica},
  pages={159 – 202},
Alexander Lytchak, and Stefan Wenger. Isoperimetric characterization of upper curvature bounds. 2018. Vol. 221. In Acta Mathematica. pp.159 – 202.
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