Skip to main content
SpringerLink
Log in

Differentiability and rigidity of Möbius groups

  • Published:
Inventiones mathematicae Aims and scope

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. Agard, S.: A geometric proof of Mostow's rigidity theorem for groups of divergence type. Acta Math.151, 231–252 (1983)

    Google Scholar 

  2. Agard, S.: Elementary properties of Möbius transformations inR n with applications to rigidity theory. University of Minnesota, Math. Rep. (mimeographed notes) No. 82-100 (1982)

  3. Agard, S.: Remarks on the boundary mapping for a Fuchsian group. (To appear)

  4. Ahlfors, L.V.: Möbius transformations in several dimensions. Mimeographed lecture notes at the University of Minnesota 1981

  5. Apanasov, B.N.: Geometrically finite groups of spatial transformations. Sib. Math. J. (Russian)23, (6) 16–27 (1982)

    Google Scholar 

  6. Beardon, A.F., Maskit, B.: Limit points of Kleinian groups and finite sided fundamental polyhedra. Acta Math.132, 1–12 (1974)

    Google Scholar 

  7. Federer, H.: Geometric measure theory. New York: Springer 1969

    Google Scholar 

  8. Garland, H., Raghunathan, M.S.: Fundamental domains for lattices in (R-)rank 1 semisimple Lie groups. Ann. Math.92, 279–326 (1970)

    Google Scholar 

  9. Gottschalk, W.H., Hedlund, G.A.: Topological dynamics. AMS Colloquium Publications XXXVI, Am. Math. Soc. 1955

  10. Lehto, O., Virtanen, K.I.: Quasiconformal mappings in the plane. Berlin-Heidelberg-New York: Springer 1973

    Google Scholar 

  11. Mostow, G.D.: Strong rigidity of locally symmetric spaces. Ann. Math. Stud., vol. 78. Princeton: Princeton University Press 1973

    Google Scholar 

  12. Näätänen, M.: Maps with continuous characteristics as a subclass of quasiconformal maps. Ann. Acad. Sci. Fenn., Ser. AI410, 1–28 (1967)

    Google Scholar 

  13. Selberg, A.: Recent developments in the theory of discontinuous groups of motions of symmetric spaces. In: Aubert, K.E., Ljunggren, W.L. (eds.), Proceedings of the 15th Scandinavian Congress, Oslo 1968. Lect. Notes Math., vol. 118, pp. 9–120. Berlin-Heidelberg-New York: Springer 1970

    Google Scholar 

  14. Sullivan, D.: On the ergodic theory at infinity of an arbitrary discrete group of hyperbolic motions. In: Riemann surfaces and related topics: Proceedings of the 1978 Stony Brook conference (I. Kra, B. Maskit, eds.), Ann. Math. Stud., vol. 97, pp. 465–496. Princeton: Princeton University Press 1981

    Google Scholar 

  15. Tukia, P.: On two-dimensional quasiconformal groups. Ann. Acad. Sci. Fenn., Ser. AI5, 73–78 (1980)

    Google Scholar 

  16. Tukia, P.: On isomorphisms of geometrically finite Möbius groups. Inst. Hautes Études Sci. Publ. Math.61, 171–214 (1985)

    Google Scholar 

  17. Tukia, P.: Rigidity theorems for Möbius groups. (To appear)

  18. Tukia, P.: On quasiconformal groups. (To appear)

  19. Wielenberg, N.J.: Discrete Möbius groups: Fundamental polyhedra and convergence. Am. J. Math.99, 861–877 (1977)

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics, University of Helsinki, SF-00100, Helsinki 10, Finland

    Pekka Tukia

Authors
  1. Pekka Tukia
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

Tukia, P. Differentiability and rigidity of Möbius groups. Invent Math 82, 557–578 (1985). https://doi.org/10.1007/BF01388870

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01388870

Search

Navigation