Skip to main content
SpringerLink
Log in

On the asymptotically PT−1 spaces

  • Published:
Acta Mathematica Sinica, English Series Aims and scope Submit manuscript

Abstract

In this note, first, we show that the asymptotic subcone, the ultralimit, the completion of an asymptotically PT−1 space are still an asymptotically PT−1 space. Secondly, we consider two kinds of metric spaces, which have been considered by Ibragimov and Gromov, respectively. We show that they are asymptotically PT−1 spaces under particular conditions, which provide some concrete examples of asymptotically PT−1 spaces.

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

Access this article

Log in via an institution

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

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Bonk, M., Heinonen, J., Koskela, P.: Uniformizing Gromov hyperbolic spaces. Astérisque, 270, (2001)

    Google Scholar 

  2. Benoist, Y.: Convexes hyperboliques et fonctions quasisymetriques (French) [Hyperbolic convex sets and quasisymmetric functions]. Publ. Math. Inst. Hautes Etudes Sci., 97, 181–237 (2003)

    Article  MATH  Google Scholar 

  3. Foertsch, T., Schroeder, V.: Hyperbolicity, CAT(-1)-spaces and the Ptolemy Inequality. Math. Ann., 350(2), 339–356 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  4. Gromov, M.: Hyperbolic groups. In Essays in Group Theory, Springer, New York, 1987

    Google Scholar 

  5. Ibragimov, Z.: Hyperbolizing metric spaces. Proc. Amer. Math. Soc., 139, 4401–4407 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  6. Kleiner, B., Leeb, B.: Rigidity of quasi-isometries for symmetric spaces and Euclidean buildings. Inst. Hautes Etudes Sci. Publ. Math., 86, 115–197 (1997)

    Article  MathSciNet  MATH  Google Scholar 

  7. Miao, R., Schroeder, V.: Hyperbolic spaces and Ptolemy Möbius structures. 2012, preprint

    Google Scholar 

  8. Nowak, P. W., Yu, G.: Large Scale Geometry, EMS Textbooks in Mathematics, European Mathematical Society, 2012

    Google Scholar 

  9. Perelman, G. Ya., Petrunin, A. M.: Quasigeodesics and gradient curves in Alexandrov spaces, preprint, (1994)

    Google Scholar 

Download references

Acknowledgements

The authors would like to thank the anonymous referees for their valuable comments and suggestions.

Author information

Authors and Affiliations

  1. College of Mathematics and Econometrics, Hu’nan University, Changsha, 410082, P. R. China

    Xin Luo, Ying Qing Xiao & Yue Ping Jiang

Authors
  1. Xin Luo
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Ying Qing Xiao
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Yue Ping Jiang
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Ying Qing Xiao.

Additional information

This work was supported by National Natural Science Foundation of China (Grant Nos. 11301165, 11371126 and 11571099)

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Luo, X., Xiao, Y.Q. & Jiang, Y.P. On the asymptotically PT−1 spaces. Acta. Math. Sin.-English Ser. 33, 1421–1430 (2017). https://doi.org/10.1007/s10114-017-5257-9

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10114-017-5257-9

Keywords

MR(2010) Subject Classification

Search

Navigation