Skip to main content
SpringerLink
Log in

An extremal problem for quasiconformal mappings and a theorem by Thurston

  • Published:
Acta Mathematica

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

References

  1. Ahlfors, L. V., On quasiconformal mappings.J. Analyse Math., 3 (1953–54), 1–58.

    Article  MathSciNet  Google Scholar 

  2. —,Lectures on Quasiconformal Mappings, Van Nostrand, Princeton (1966).

    MATH  Google Scholar 

  3. Bers, L., Quasiconformal mappings and Teichmüller's theorem.Analytic Functions. Princeton University Press, Princeton (1960), 89–119.

    Google Scholar 

  4. —, Fiber spaces over Teichmüller spaces.Acta Math., 130 (1973), 89–126.

    Article  MathSciNet  MATH  Google Scholar 

  5. —, A remark on Mumford's compactness theorem.Israel J. Math., 12 (1972), 400–407.

    MathSciNet  MATH  Google Scholar 

  6. —, Uniformization, moduli and Kleinian groups.Bull. London Math. Soc., 4 (1972), 257–300.

    MathSciNet  MATH  Google Scholar 

  7. —, Nielsen extensions of Riemann surfaces.Ann. Acad. Sci. Fenn., 2 (1976), 17–22.

    MathSciNet  Google Scholar 

  8. Busemann, H.,Metric Methods in Finsler Geometry and in the Foundations of Geometry. Ann. of Math. Studies, 8, Princeton Univ. Press, Princeton (1942).

    MATH  Google Scholar 

  9. Earle, C. J., Teichmüller theory.Discrete Groups and Automorphic Functions (edited by W. J. Harvey). Academic Press, London-New York-San Francisco (1977), 143–162.

    Google Scholar 

  10. —, Teichmüller, distance is differentiable.Duke Math. J., 44 (1977) 389–398.

    Article  MathSciNet  MATH  Google Scholar 

  11. Epstein, D. B., Curves on two-manifolds and isotopes.Acta Math., 115 (1965), 83–107.

    Article  Google Scholar 

  12. Fenchel, W., Estensioni di gruppi e trasformazioni periodiche delle superficie.Rend. Lincei, 5 (1948), 326–329.

    MathSciNet  MATH  Google Scholar 

  13. Kravetz, S., On the geometry of Teichmüller spaces and the structures of their modular groups.Ann. Acad. Sci. Fenn., 278 (1959), 1–35.

    MathSciNet  Google Scholar 

  14. Linch, M. R., On metrics in Teichmüller space. Ph.D. Thesis, Columbia University (1971).

  15. Mangler, W., Die Klassen topologischer Abbildungen einer geschlossenen Fläche auf sich.Math. Z., 44 (1939), 541–554.

    Article  MathSciNet  Google Scholar 

  16. Matelski, J. P., A compactness theorem for Fuchsian groups of the second kind.Duke Math. J., 43 (1976), 829–840.

    Article  MathSciNet  MATH  Google Scholar 

  17. Mori, A., On an absolute constant in the theory of quasi-conformal mappings.J. Math. Soc. Japan, 8 (1956), 156–166.

    Article  MathSciNet  MATH  Google Scholar 

  18. Mumford, D., A remark on Mahler's compactness theorem.Proc. Amer. Math. Soc., 28 (1971), 289–294.

    Article  MathSciNet  MATH  Google Scholar 

  19. Teichmüller, O., Extremale quasikonforme Abbildungen und quadratische Differentiale.Abh. Pseuss. Akad. Wiss., 22 (1939).

  20. Teichmüller, O., Bestimmung der extremalen quasikonformen Abbildungen bei geschlossenen orientierten Riemannschen Flächen. Ibid.Abh. Preuss. Akad. Wiss., 4 (1943).

  21. Thurston, W. P., On the geometry and dynamics of diffeomorphisms of surfaces, I. To appear.

  22. Wolpert, S., The length spectrum of a compact Riemann surface, I. To appear.

Download references

Author information

Authors and Affiliations

  1. Columbia University, New York

    Lipman Bers

Authors
  1. Lipman Bers
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

To Lars V. Ahlfors, on his 70th birthday

This work has been partially supported by the National Science Foundation under grant number NSF MCS76-08478.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Bers, L. An extremal problem for quasiconformal mappings and a theorem by Thurston. Acta Math. 141, 73–98 (1978). https://doi.org/10.1007/BF02545743

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02545743

Keywords

Search

Navigation