Skip to main content
Log in

Extremal polygonal quasiconformal mappings and biLipschitz mappings

  • Articles
  • Published:
Science China Mathematics Aims and scope Submit manuscript

Abstract

We show that the extremal polygonal quasiconformal mappings are biLipschitz with respect to the hyperbolic metric in the unit disk.

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.

Similar content being viewed by others

References

  1. Ahlfors L V. Lectures on Quasiconformal Mappings. Princeton: Van Nostrand, 1966

    MATH  Google Scholar 

  2. Bishop C J. BiLipschitz approximations of quasiconformal maps. Ann Acad Sci Fenn Math, 2002, 27: 97–108

    MATH  MathSciNet  Google Scholar 

  3. Douady A, Earle C. Conformally natural extensions of homeomorphisms of circle. Acta Math, 1986, 157: 23–48

    Article  MATH  MathSciNet  Google Scholar 

  4. Epstein A, Marden A. Convex hulls in hyperbolic space, a theorem of Sullivan, and measured pleated surfaces. In: Analytical and Geometric Aspects of Hyperbolic Space. Cambridge: Cambridge University Press, 1987, 113–253

    Google Scholar 

  5. Gardiner F P, Lakic N. Quasiconformal Teichmüller Theory. In: Mathematical Surveys and Monographs, vol. 76. Providence, RI: American Mathematical Society, 2000

    Google Scholar 

  6. Reich E, Strebel K. Extremal Quasiconformal Mappings with Given Boundary Values. In: Contributions to Analysis. New York: Academic Press, 1974, 375–391

    Google Scholar 

  7. Strebel K. Quadratic Differentials. Berlin-New York: Springer-Verlag, 1984

    MATH  Google Scholar 

  8. Strebel K. Extremal quasiconformal mappings. Results Math, 1986, 10: 168–210

    MATH  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to HuaYing Huang.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Huang, H., Wu, S. Extremal polygonal quasiconformal mappings and biLipschitz mappings. Sci. China Math. 53, 1275–1282 (2010). https://doi.org/10.1007/s11425-010-0076-9

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11425-010-0076-9

Keywords

MSC(2000)

Navigation