Skip to main content
SpringerLink
Log in

Coarsely Bilipschitz Continuity of Inversions with Respect to Distance Ratio Metrics in Metric Spaces

  • Published:
Results in Mathematics Aims and scope Submit manuscript

Abstract

In this paper, we prove that the inversions in metric spaces are coarsely bilipschitz continuous with respect to distance ratio metric.

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. Astrisque 270, 1–99 (2001)

    MATH  Google Scholar 

  2. Buckley, M.S., Herron, A.D., Xie, X.: Metric space inversions, quasihyperbolic distance, and uniform spaces. Indiana Univ. Math. J. 57, 837–890 (2008)

    MathSciNet  MATH  Google Scholar 

  3. Gehring, F.W., Osgood, B.G.: Uniform domains and the quasihyperbolic metric. J. Anal. Math. 36, 50–74 (1979)

    Article  MathSciNet  Google Scholar 

  4. Gehring, F.W., Palka, B.P.: Quasiconformally homogeneous domains. J. Anal. Math. 30, 172–199 (1976)

    Article  MathSciNet  Google Scholar 

  5. Seittenranta, P.: Möbius-invariant metrics. Math. Proc. Camb. Philos. Soc. 125, 511–533 (1999)

    Article  MathSciNet  Google Scholar 

  6. Väisälä, J.: Quasi-Möbius maps. J. Anal. Math. 44, 218–234 (1984/1985)

  7. Väisälä, J.: Free quasiconformality in Banach spaces. I. Ann. Acad. Sci. Fenn. Ser. A I Math. 15, 355–379 (1990)

    Article  MathSciNet  Google Scholar 

  8. Väisälä, J.: Free quasiconformality in Banach spaces. II. Ann. Acad. Sci. Fenn. Ser. A I Math. 16, 255–310 (1991)

    Article  MathSciNet  Google Scholar 

Download references

Acknowledgements

This work of the first author (Mrs. Tiantian Guan) was completed during her visit to IIT Madras, India, and the visit was supported by the award of “Research Training Fellowship–Developing Countries Scientists (RTF–DCS),” DCS/2018/000047, Department of Science and Technology, Government of India. The second author (Mrs. Manzi Huang) was partly supported by NNSF of China under the Number 11822105, and the fourth author (Mr. Xiantao Wang) was partly supported by NNSFs of China under the Numbers 12071121 and 11720101003 and the Project under the Number 2018KZDXM034.

Author information

Authors and Affiliations

  1. Department of Mathematics, Shantou University, Shantou, 515063, Guangdong, People’s Republic of China

    Tiantian Guan

  2. MOE-LCSM, School of Mathematics and Statistics, Hunan Normal University, Changsha, 410081, Hunan, People’s Republic of China

    Manzi Huang & Xiantao Wang

  3. School of Mathematical Science, Qufu Normal University, Qufu, 273165, Shandong, People’s Republic of China

    Manzi Huang

  4. Department of Mathematics, Indian Institute of Technology Madras, Chennai, 600036, India

    Saminathan Ponnusamy

Authors
  1. Tiantian Guan
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Manzi Huang
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Saminathan Ponnusamy
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Xiantao Wang
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Saminathan Ponnusamy.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Guan, T., Huang, M., Ponnusamy, S. et al. Coarsely Bilipschitz Continuity of Inversions with Respect to Distance Ratio Metrics in Metric Spaces. Results Math 76, 50 (2021). https://doi.org/10.1007/s00025-021-01352-2

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/s00025-021-01352-2

Keywords

Mathematics Subject Classification

Search

Navigation