Skip to main content
Log in

Action of Möbius transformations on homeomorphisms: Stability and rigidity

  • Published:
Geometric & Functional Analysis GAFA Aims and scope Submit manuscript

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.

Institutional subscriptions

References

  1. S. Agard, A geometric proof of Mostow's rigidity theorem for groups of divergence type, Acta Math. 151 (1983), 321–252.

    Google Scholar 

  2. S. Agard, Mostow rigidity on the line: A survey, in “Holomorphic Functions and Moduli, II” (D. Drasin, C. Earle, F. Gehring, I. Kra, A. Marden, eds), MSRI Publications 11 (1988), 1–12.

  3. K. Astala, M. Zinsmeister, Mostow rigidity and fuchsian groups, C.R. Acad. Sci. Paris, t. 311, Série I (1990), 301–306.

    Google Scholar 

  4. R. Benedetti, C. Petronio, Lectures on Hyperbolic Geometry, Universitext, Springer-Verlag, 1993.

  5. A. Douady, C. Earle, Conformally natural extension of homeomorphisms of the circle, Acta Math. 157 (1986), 23–48.

    Google Scholar 

  6. G.B. Folland, Harmonic analysis in phase space, Ann. of Math. Studies, 122, Princeton University Press, 1989.

  7. M. Gromov, P. Pansu, Rigidity of lattices: an introduction, in “Geometric Topology: Recent Developments, Montecatini Terme, 1990” (P. de Bartolomeis, F. Tricerri, eds.) Springer Lecture Notes in Math. 1504 (1991) 39–137.

  8. S.P. Kerckhoff, The Nielsen realization problem, Ann. of Math. 117 (1983), 235–265.

    Google Scholar 

  9. O. Lehto, Univalent functions and Teichmüller space, Graduate Texts in Math. 109, Springer-Verlag, 1987.

  10. G.D. Mostow, Quasi-conformal mappings inn-space and the rigidity of hyperbolic space forms, Publ. Math. IHES 34 (1968), 53–104.

    Google Scholar 

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

  12. R. Penner, Universal constructions in Teichmüller theory, Advances in Math. 98 (1993), 143–215.

    Google Scholar 

  13. G. Prasad, Strong rigidity of Q-rank 1 lattlices, Inventiones Math. 21 (1973), 255–286.

    Google Scholar 

  14. S. Rickman, Quasiregular Mappings, Ergebnisse der Mathematik, 3 Folge, Bd. 26, Springer-Verlag, 1993.

  15. W. Rudin, Function Theory in the Unit Ball of Cn, Grundlehren der Math. Wiss. 241, Springer-Verlag, 1980.

  16. E.M. Stein, Singular Integrals and Differentiability Properties of Functions, Princeton Math. Series 30, Princeton University Press, 1970.

  17. D. Sullivan, 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. of Math. Studies 97 (1981), 465–496.

  18. P. Tukia, Differentiability and rigidity of Möbius groups, Inventiones Math. 82 (1985), 557–578.

    Google Scholar 

  19. P. Tukia, Mostow-rigidity and non-compact hyperbolic manifolds, Quart. J. Math. Oxford (2), 42 (1991), 219–226.

    Google Scholar 

  20. P. Tukia, Letter to the author, January 4, 1994.

  21. J. Väisälä, Lectures onn-dimensional Quasiconformal Mappings, Lecture Notes in Mathematics 229, Springer-Verlag, 1971.

Download references

Author information

Authors and Affiliations

Authors

Additional information

To M. Gromov at his 50-th birthday

Supported in part by the NSF Grant DMS 9401284.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Ivanov, N.V. Action of Möbius transformations on homeomorphisms: Stability and rigidity. Geometric and Functional Analysis 6, 79–119 (1996). https://doi.org/10.1007/BF02246768

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02246768

Navigation