Mathematische Zeitschrift

, Volume 274, Issue 1–2, pp 461–470 | Cite as

A flat strip theorem for ptolemaic spaces

  • Renlong Miao
  • Viktor SchroederEmail author

Main result and motivation

A metric space \((X,d)\)


Parallel Line Short Proof Isometric Embedding Geodesic Segment Strict Convexity 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


  1. 1.
    Buckley, S.M., Falk, K., Wraith, D.J.: Ptolemaic spaces and \(\operatorname{CAT}(0)\). Glasgow J. Math. 51, 301–314 (2009)MathSciNetzbMATHCrossRefGoogle Scholar
  2. 2.
    Berg, I.D., Nikolaev, I.G.: Quasilinearization and curvature of Aleksandrov spaces. Geom. Dedicata 133, 195–218 (2008)MathSciNetzbMATHCrossRefGoogle Scholar
  3. 3.
    Buyalo, S., Schroeder, V.: Möbius structures and Ptolemy spaces: boundary at infinity of complex hyperbolic spaces. arXiv:1012.1699 (2010)Google Scholar
  4. 4.
    Enflo, P.: On the nonexistence of uniform homeomorphisms between \(L_p\)-spaces. Ark. Mat. 8, 103–105 (1969)MathSciNetCrossRefGoogle Scholar
  5. 5.
    Foertsch, T., Lytchak, A., Schroeder, V.: Nonpositive curvature and the Ptolemy inequality. Int. Math. Res. Not. IMRN 22, 15 (2007)Google Scholar
  6. 6.
    Foertsch, Th, Schroeder, V.: Hyperbolicity, \((-1)\)-spaces and the Ptolemy Inequality. Math. Ann. 350(2), 339356 (2011)MathSciNetCrossRefGoogle Scholar
  7. 7.
    Foertsch, Th, Schroeder, V.: Group actions on geodesic Ptolemy spaces. Trans. Am. Math. Soc. 363(6), 28912906 (2011)MathSciNetCrossRefGoogle Scholar
  8. 8.
    Hitzelberger, P., Lytchak, A.: Spaces with many affine functions. Proc. AMS 135(7), 2263–2271 (2007)MathSciNetzbMATHCrossRefGoogle Scholar
  9. 9.
    Sato, T.: An alternative proof of Berg and Nikolaev’s characterization of \((0)\)-spaces via quadrilateral inequality. Arch. Math. 93(5), 487490 (2009)CrossRefGoogle Scholar
  10. 10.
    Schoenberg, I.J.: A remark on M. M. Day’s characterization of inner-product spaces and a conjecture of L. M. Blumenthal. Proc. Am. Math. Soc. 3, 961–964 (1952)MathSciNetzbMATHGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  1. 1.Institut für MathematikUniversität ZürichZurichSwitzerland

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