References
Buckley, S.M., Falk, K., Wraith, D.J.: Ptolemaic spaces and \(\operatorname{CAT}(0)\). Glasgow J. Math. 51, 301–314 (2009)
Berg, I.D., Nikolaev, I.G.: Quasilinearization and curvature of Aleksandrov spaces. Geom. Dedicata 133, 195–218 (2008)
Buyalo, S., Schroeder, V.: Möbius structures and Ptolemy spaces: boundary at infinity of complex hyperbolic spaces. arXiv:1012.1699 (2010)
Enflo, P.: On the nonexistence of uniform homeomorphisms between \(L_p\)-spaces. Ark. Mat. 8, 103–105 (1969)
Foertsch, T., Lytchak, A., Schroeder, V.: Nonpositive curvature and the Ptolemy inequality. Int. Math. Res. Not. IMRN 22, 15 (2007)
Foertsch, Th, Schroeder, V.: Hyperbolicity, \((-1)\)-spaces and the Ptolemy Inequality. Math. Ann. 350(2), 339356 (2011)
Foertsch, Th, Schroeder, V.: Group actions on geodesic Ptolemy spaces. Trans. Am. Math. Soc. 363(6), 28912906 (2011)
Hitzelberger, P., Lytchak, A.: Spaces with many affine functions. Proc. AMS 135(7), 2263–2271 (2007)
Sato, T.: An alternative proof of Berg and Nikolaev’s characterization of \((0)\)-spaces via quadrilateral inequality. Arch. Math. 93(5), 487490 (2009)
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)
Author information
Authors and Affiliations
Corresponding author
Rights 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
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00209-012-1078-9