Skip to main content
Log in

A flat strip theorem for ptolemaic spaces

  • Published:
Mathematische Zeitschrift Aims and scope Submit manuscript

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

References

  1. Buckley, S.M., Falk, K., Wraith, D.J.: Ptolemaic spaces and \(\operatorname{CAT}(0)\). Glasgow J. Math. 51, 301–314 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  2. Berg, I.D., Nikolaev, I.G.: Quasilinearization and curvature of Aleksandrov spaces. Geom. Dedicata 133, 195–218 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  3. Buyalo, S., Schroeder, V.: Möbius structures and Ptolemy spaces: boundary at infinity of complex hyperbolic spaces. arXiv:1012.1699 (2010)

  4. Enflo, P.: On the nonexistence of uniform homeomorphisms between \(L_p\)-spaces. Ark. Mat. 8, 103–105 (1969)

    Article  MathSciNet  Google Scholar 

  5. Foertsch, T., Lytchak, A., Schroeder, V.: Nonpositive curvature and the Ptolemy inequality. Int. Math. Res. Not. IMRN 22, 15 (2007)

    Google Scholar 

  6. Foertsch, Th, Schroeder, V.: Hyperbolicity, \((-1)\)-spaces and the Ptolemy Inequality. Math. Ann. 350(2), 339356 (2011)

    Article  MathSciNet  Google Scholar 

  7. Foertsch, Th, Schroeder, V.: Group actions on geodesic Ptolemy spaces. Trans. Am. Math. Soc. 363(6), 28912906 (2011)

    Article  MathSciNet  Google Scholar 

  8. Hitzelberger, P., Lytchak, A.: Spaces with many affine functions. Proc. AMS 135(7), 2263–2271 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  9. Sato, T.: An alternative proof of Berg and Nikolaev’s characterization of \((0)\)-spaces via quadrilateral inequality. Arch. Math. 93(5), 487490 (2009)

    Article  Google Scholar 

  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)

    MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Viktor Schroeder.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Miao, R., Schroeder, V. A flat strip theorem for ptolemaic spaces. Math. Z. 274, 461–470 (2013). https://doi.org/10.1007/s00209-012-1078-9

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00209-012-1078-9

Keywords

Navigation