Journal d’Analyse Mathématique

, Volume 46, Issue 1, pp 318–346 | Cite as

On quasiconformal groups

  • Pekka Tukia


Hyperbolic Space Conformal Structure Radial Point Complex Dilatation Hyperbolic Line 
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  1. 1.
    L. V. Ahlfors,A somewhat new approach to quasiconformal mappings in R n, inComplex Analysis, Kentucky 1976, J. D. Buckholtz and T. J. Suffridge, eds., Lecture Notes in Mathematics599, Springer-Verlag, Berlin, 1977, pp. 1–6.Google Scholar
  2. 2.
    A. Beurling and L. Ahlfors,The boundary correspondence under quasiconformal mappings, Acta Math.96 (1956), 125–142.MATHCrossRefMathSciNetGoogle Scholar
  3. 3.
    J. Dieudonné,Foundations of Modern Analysis, Academic Press, New York, 1960.MATHGoogle Scholar
  4. 4.
    H. Fédérer,Geometric Measure Theory, Springer-Verlag, Berlin, 1969.MATHGoogle Scholar
  5. 5.
    F. W. Gehring,The L p -integrabitity of the partial derivatives of a quasi-conformal mapping, Acta Math.130 (1973), 265–277.MATHCrossRefMathSciNetGoogle Scholar
  6. 6.
    F. W. Gehring, Extremal length definitions for the conformal capacity of rings in space, Michigan Math. J.9 (1962), 137–150.MATHCrossRefMathSciNetGoogle Scholar
  7. 7.
    F. W. Gehring and J. C. Kelly,Quasi-conformal mappings and Lebesgue density, inDiscontinuous Groups and Riemann Surfaces, Proceedings of the 1973 Conference at the University of Maryland, L. Greenberg, ed., Ann. Math. Studies79, Princeton University Press, 1974, pp. 171–179.Google Scholar
  8. 8.
    F. W. Gehring and B. P. Palka,Quasiconformally homogeneous domains, J. Analyse Math.30 (1976), 172–199.MATHMathSciNetCrossRefGoogle Scholar
  9. 9.
    M. Gromow,Hyperbolic manifolds, groups and actions, inRiemann Surfaces and Related Topics : Proceedings of the 1978 Stony Brook Conference, I. Kra and B. Maskit, eds., Ann. Math. Studies97, Princeton University Press, 1981, pp. 183–213.Google Scholar
  10. 10.
    S. Helgason,Differential Geometry, Lie Groups, and Symmetric Spaces, Academic Press, New York, 1978.MATHGoogle Scholar
  11. 11.
    A. Hinkkanen,Uniformly quasisymmetric groups, Proc. London Math. Soc. (3)51 (1985), 318–338.MATHCrossRefMathSciNetGoogle Scholar
  12. 12.
    O. Lehto and K. I. Virtanen,Quasiconformal Mappings in the Plane, Springer-Verlag, Berlin, 1973.MATHGoogle Scholar
  13. 13.
    J. Lelong-Ferrand,Transformations conformes et quasi-conformes des variétés riemanniennes compactes, Acad. R. Belg. Cl. Sci. Mém. Coll. in 8‡ (2)39, no. 5 (1971), 1–44.MathSciNetGoogle Scholar
  14. 14.
    H. Maass,Siegel’s Modular Forms and Dirichlet Series, Lecture Notes in Mathematics216, Springer-Verlag, Berlin, 1971.MATHGoogle Scholar
  15. 15.
    G. J. Martin,iscrete quasiconformal groups that are not the quasiconformal conjugates of Möbius groups, Ann. Acad. Sci. Fenn. Ser. A I11 (1986).Google Scholar
  16. 16.
    G. D. Mostow,Quasi-conformal mappings in n-space and the rigidity of hyperbolic space forms, Inst. Hautes Etudes Sci. Publ. Math.34 (1968), 53–104.MATHCrossRefMathSciNetGoogle Scholar
  17. 17.
    D. Sullivan,On the ergodic theory at infinity of an arbitrary discrete group of hyperbolic motions, inRiemann Surfaces and Related Topics: Proceedings of the 1978 Stony Brook Conference, I. Kra and B. Maskit, eds., Ann. Math. Studies 97, Princeton University Press, 1981, pp. 465–496.Google Scholar
  18. 18.
    P. Tukia,On two-dimensional quasiconformal groups, Ann. Acad. Sci. Fenn. Ser. A I5 (1980), 73–78.MathSciNetMATHGoogle Scholar
  19. 19.
    P. Tukia,A quasiconformal group not isomorphic to a Möbius group, Ann. Acad. Sci. Fenn. Ser. A I6 (1981), 149–160.MathSciNetMATHGoogle Scholar
  20. 20.
    P. Tukia,Quasiconformal extension of quasisymmetric mappings compatible with a Möbius group, Acta Math.154 (1985), 153–193.MATHCrossRefMathSciNetGoogle Scholar
  21. 21.
    P. Tukia,Differentiability and rigidity of Möbius groups, Invent. Math.82 (1985), 557–578.MATHCrossRefMathSciNetGoogle Scholar
  22. 22.
    P. Tukia and J. VÄisÄlÄ,A remark on 1-quasiconformal mappings, Ann. Acad. Sci. Fenn. Ser. A I10 (1985), 561–562.MATHGoogle Scholar
  23. 23.
    J. VÄisÄlÄ,Lectures on n-Dimensional Quasiconformal Mappings, Lecture Notes in Mathematics229, Springer-Verlag, Berlin, 1971.MATHGoogle Scholar

Copyright information

© Hebrew University of Jerusalem 1986

Authors and Affiliations

  • Pekka Tukia
    • 1
    • 2
  1. 1.University of HelsinkiHelsinkiFinland
  2. 2.Institut Mittag-LefflerDjursholmSweden

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