Archiv der Mathematik

, Volume 99, Issue 1, pp 81–89 | Cite as

Möbius characterization of hemispheres

  • Thomas FoertschEmail author
  • Viktor Schroeder


In this paper we generalize the Möbius characterization of metric spheres as obtained in Foertsch and Schroeder [4] to a corresponding Möbius characterization of metric hemispheres.


Banach Space Open Subset Interior Point Half Space Triangle Inequality 
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  1. 1.
    Th. Foertsch, A. Lytchak, and V. Schroeder, Nonpositive curvature and the Ptolemy inequality, Int. Math. Res. Not. IMRN 2007, 15 pp.Google Scholar
  2. 2.
    Foertsch Th., Schroeder V.: Hyperbolicity, CAT(−1)-spaces and the Ptolemy Inequality. Math. Ann. 350, 339–356 (2011)MathSciNetzbMATHCrossRefGoogle Scholar
  3. 3.
    Foertsch Th., Schroeder V.: Group actions on geodesic Ptolemy spaces. Trans. Amer. Math. Soc. 363, 2891–2906 (2011)MathSciNetzbMATHCrossRefGoogle Scholar
  4. 4.
    Th. Foertsch and V. Schroeder, Metric Möbius Geometry and the Characterization of Spheres, to appear in Manuscripta Math.Google Scholar
  5. 5.
    Th. Foertsch and V. Schroeder, Ptolemy Circles and Ptolemy Segments, Archiv der Mathematik, to appear.Google Scholar
  6. 6.
    Hitzelberger P., Lytchak A.: Spaces with many affine functions Proc. AMS 135, 2263–2271 (2007)MathSciNetzbMATHCrossRefGoogle Scholar
  7. 7.
    Schoenberg I.J.: A remark on M. M. Day’s characterization of inner-product spaces and a conjecture of L. M. Blumenthal. Proc. Amer. Math. Soc. 3, 961–964 (1952)MathSciNetzbMATHGoogle Scholar

Copyright information

© Springer Basel AG 2012

Authors and Affiliations

  1. 1.Institut für MathematikUniversität ZürichZurichSwitzerland

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