Ptolemy circles and Ptolemy segments

DOI10.1007/S00013-012-0398-7zbMath1267.53078OpenAlexW2000854011MaRDI QIDQ438608

Viktor Schroeder, Thomas Foertsch

Publication date: 31 July 2012

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

Full work available at URL: https://www.zora.uzh.ch/id/eprint/71199/11/ZORA_NL_71199.pdf

zbMATH Keywords

Ptolemy metric space\(CAT(-1)\)-spaceMöbius homeomorphismPtolemy circlePtolemy's theorem

Mathematics Subject Classification ID

Möbius geometries (51B10) Topological geometries on manifolds (51H20) Direct methods ((G)-spaces of Busemann, etc.) (53C70)

Related Items (2)

Möbius characterization of hemispheres ⋮ SRA-free condition by Zolotov for self-contracted curves and nondegeneracy of the zz-distance for Möbius structures on the circle

Cites Work

• Hyperbolicity, CAT(\(-1\))-spaces and the Ptolemy inequality
• Elements of asymptotic geometry
• Conformal structure on the boundary and geodesic flow of a \(\text{CAT}(-1)\)-space
• Metric Möbius geometry and a characterization of spheres
• Group actions on geodesic Ptolemy spaces
• Spaces with many affine functions
• 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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