Skip to main content
SpringerLink
Log in

Bi-Lipschitz concordance implies bi-Lipschitz isotopy

  • Published:
Monatshefte für Mathematik Aims and scope Submit manuscript

Abstract

We modify the proof of an earlier result of ours to deforming topological, bi-Lipschitz, and quasiconformal embeddings of an open subsetU ofR n which now are of small uniform distance from the inclusion map. As an application we show that two bi-Lipschitz homeomorphismsf 0,f 1:R n→Rn are bi-Lipschitz isotopic if and only ifd(f 0,f 1)<∞.

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. Luukkainen, J.: Respectful deformation of bi-Lipschitz and quasisymmetric embeddings. Ann. Acad. Sci. Fenn. Ser. A I Math.13, 137–177 (1988).

    Google Scholar 

  2. Siebenmann, L. C.: Deformation of homeomorphisms on stratified sets. Comment. Math. Helv.47, 123–163 (1972).

    Google Scholar 

  3. Tukia, P., Väisälä, J.: Quasisymmetric embeddings of metric spaces. Ann. Acad. Sci. Fenn. Ser. A I Math.5, 97–114 (1980).

    Google Scholar 

  4. Tukia, P. Väisälä, J.: Quasiconformal extension from dimensionn ton+1. Ann. of Math. (2)115, 331–348 (1982).

    Google Scholar 

  5. Väisälä, J.: Lectures onn-dimensional quasiconformal mappings. Lecture Notes in Math.229, Berlin-Heidelberg-New York: Springer. 1971.

    Google Scholar 

  6. Väisälä, J.: Quasiconformal concordance. Mh. Math.107, 155–168 (1989).

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics, University of Helsinki, Hallituskatu 15, SF-00100, Helsinki, Finland

    Jouni Luukkainen

Authors
  1. Jouni Luukkainen
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

Research supported in part by a grant from the Institut Mittag-Leffler.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Luukkainen, J. Bi-Lipschitz concordance implies bi-Lipschitz isotopy. Monatshefte für Mathematik 111, 35–46 (1991). https://doi.org/10.1007/BF01299275

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01299275

Keywords

Search

Navigation