An alternative proof of Berg and Nikolaev's characterization of \(CAT(0)\)-spaces via quadrilateral inequality

DOI10.1007/s00013-009-0057-9zbMath1221.53100OpenAlexW2062971663MaRDI QIDQ1042431

Takashi Sato

Publication date: 14 December 2009

Published in: Archiv der Mathematik (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00013-009-0057-9

zbMATH Keywords

metric spaceCAT(0)-spacequadrilateral inequality

Mathematics Subject Classification ID

Global surface theory (convex surfaces à la A. D. Aleksandrov) (53C45) Synthetic differential geometry (51K10)

Related Items (13)

Characterization of Aleksandrov spaces of curvature bounded above by means of the metric Cauchy-Schwarz inequality ⋮ On a question of Gromov about the Wirtinger inequalities ⋮ \(K\)-Euler's inequality in Aleksandrov's \(\mathrm{CAT}(K)\) space ⋮ Old and new challenges in Hadamard spaces ⋮ A non-geodesic analogue of Reshetnyak's majorization theorem ⋮ A rigidity theorem in Alexandrov spaces with lower curvature bound ⋮ An intrinsic characterization of five points in a CAT(0) space ⋮ A flat strip theorem for Ptolemaic spaces ⋮ Hlawka's functional inequality ⋮ Snowflake universality of Wasserstein spaces ⋮ No dimension reduction for doubling subsets of \(\ell_q\) when \(q>2\) revisited ⋮ Nonpositive curvature is not coarsely universal ⋮ The quasi-hyperbolicity constant of a metric space

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• A note on Markov type constants
• Sobolev spaces and harmonic maps for metric space targets
• Quasilinearization and curvature of Aleksandrov spaces
• On the nonexistence of uniform homeomorphisms between \(L^ p\)-spaces
• Reductive groups over a local field
• Nonpositive Curvature and the Ptolemy Inequality
• Metric structures for Riemannian and non-Riemannian spaces. Transl. from the French by Sean Michael Bates. With appendices by M. Katz, P. Pansu, and S. Semmes. Edited by J. LaFontaine and P. Pansu

This page was built for publication: An alternative proof of Berg and Nikolaev's characterization of \(CAT(0)\)-spaces via quadrilateral inequality