Characterization of Aleksandrov spaces of curvature bounded above by means of the metric Cauchy-Schwarz inequality

DOI10.1307/mmj/1519095621zbMath1402.53027OpenAlexW2789492361WikidataQ130208125 ScholiaQ130208125MaRDI QIDQ1654428

Igor G. Nikolaev, I. David Berg

Publication date: 8 August 2018

Published in: Michigan Mathematical Journal (Search for Journal in Brave)

Full work available at URL: https://projecteuclid.org/euclid.mmj/1519095621

Mathematics Subject Classification ID

Global Riemannian geometry, including pinching (53C20) Global surface theory (convex surfaces à la A. D. Aleksandrov) (53C45) Synthetic differential geometry (51K10)

Related Items (4)

Geometry of Data ⋮ Nonpositive curvature is not coarsely universal ⋮ Moduli of regularity and rates of convergence for Fejér monotone sequences ⋮ Topology and curvature of metric spaces

Cites Work

• An alternative proof of Berg and Nikolaev's characterization of \(CAT(0)\)-spaces via quadrilateral inequality
• Spaces with bounded curvature and distance geometry
• A metric characterization of Riemannian spaces
• On a distance between directions in an Aleksandrov space of curvature \(\leq K\)
• \(K\)-Euler's inequality in Aleksandrov's \(\mathrm{CAT}(K)\) space
• Quasilinearization and curvature of Aleksandrov spaces
• Roundness properties of groups.
• On the nonexistence of uniform homeomorphisms between \(L^ p\)-spaces
• Reductive groups over a local field
• Nonpositive Curvature and the Ptolemy Inequality
• A Remark on M. M. Day's Characterization of Inner-Product Spaces and a Conjecture of L. M. Blumenthal
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