PTOLEMAIC SPACES AND CAT(0)

DOI10.1017/S0017089509004984zbMath1171.53024OpenAlexW2032141101WikidataQ29394975 ScholiaQ29394975MaRDI QIDQ3633315

Kurt Falk, Stephen M. Buckley, David J. Wraith

Publication date: 18 June 2009

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

Full work available at URL: https://doi.org/10.1017/s0017089509004984

zbMATH Keywords

Riemannian manifoldCAT(0) spaceFinsler manifoldPtolemaic space

Mathematics Subject Classification ID

Metric geometry (51F99) Global Riemannian geometry, including pinching (53C20) Global differential geometry of Finsler spaces and generalizations (areal metrics) (53C60)

Related Items (19)

Fixed point theorems for some generalized nonexpansive mappings in Ptolemy spaces ⋮ On quasisymmetric mappings in semimetric spaces ⋮ Best constants for metric space inversion inequalities ⋮ Geodesic Ptolemy spaces and fixed points ⋮ Fixed point theorems for generalized nonexpansive mappings in hyperbolic spaces ⋮ The Four Point Condition: An Elementary Tropicalization of Ptolemy’s Inequality ⋮ Metric Möbius geometry and a characterization of spheres ⋮ A note on generalized four-point inequality ⋮ A flat strip theorem for Ptolemaic spaces ⋮ Möbius characterization of the boundary at infinity of rank one symmetric spaces ⋮ The Ptolemaean inequality in the closure of complexhyperbolic planes ⋮ Generalized angles in ptolemaic Möbius structures. II ⋮ Group actions on geodesic Ptolemy spaces ⋮ Cross-ratios and the Ptolemaean inequality in boundaries of symmetric spaces of rank 1 ⋮ On Ptolemaic metric simplicial complexes ⋮ Hyperbolizing hyperspaces ⋮ Snowflake universality of Wasserstein spaces ⋮ Hyperbolic metrics on open subsets of Ptolemaic spaces with sharp parameter bounds ⋮ Multi-valued version of \(SCC\), \(SKC\), \(KSC\), and \(CSC\) conditions in Ptolemy metric spaces

Cites Work

• Unnamed Item
• Ptolemy's inequality, chordal metric, multiplicative metric
• The Ptolemaic inequality in Hilbert geometries
• CONVEX REGIONS IN THE GEOMETRY OF PATHS
• A Panoramic View of Riemannian Geometry
• A Remark on M. M. Day's Characterization of Inner-Product Spaces and a Conjecture of L. M. Blumenthal

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