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Quasiconformal Mappings and Analysis pp 369–374Cite as

Questions on Quasiconformal Maps in Space

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Abstract

The purpose of this article is to list miscellaneous open questions on quasiconformal maps in R n

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References

  1. Ahlfors, L.V.Lectures on quasiconformal mappingsVan Nostrand, 1966.

    MATH  Google Scholar 

  2. Alestalo, P., Väisälä, J. Uniform domains of higher order III Ann. Acad. Sci. Fenn. Ser. AI Math., to appear.

    Google Scholar 

  3. Anderson, G., Vamanamurthy, M.K., Vuorinen, M. Dimension-free quasiconformal distortion in n-space, Trans. Amer. Math. Soc. 297 (1986), 687–706.

    MathSciNet  MATH  Google Scholar 

  4. Astala, K., Area distortion of quasiconformal mappings, Acta Math. 173 (1994), 37–60.

    Article  MathSciNet  MATH  Google Scholar 

  5. Beurling, A., Ahlfors, L. The boundary correspondence under quasiconformal mappings, Acta Math. 96 (1956), 125–142.

    Article  MathSciNet  MATH  Google Scholar 

  6. Bojarski, B.V. Homeomorphic solutions of a Beltrami system, Dokl. Akad. Nauk. SSSR 102 (1955), 661–664.

    MathSciNet  Google Scholar 

  7. Bojarski, B.V., Iwaniec, T. Another approach to Liouville theorem, Math. Nadir. 107 (1982), 253–262.

    MathSciNet  MATH  Google Scholar 

  8. Buczolich, Z. Density points and bi-Lipschitz functions in R m, Proc. Amer. Math. Soc. 116(1992), 53–59.

    MathSciNet  MATH  Google Scholar 

  9. Gehring, F.W. Rings and quasiconformal mappings in space, Trans. Amer. Math. Soc. 103(1962), 353–393.

    Article  MathSciNet  MATH  Google Scholar 

  10. Gehring, F.W. The L p -integrability of the partial derivatives of a quasi-conformal mapping, Acta Math. 130(1973), 265–277.

    Article  MathSciNet  MATH  Google Scholar 

  11. Kühnau, R. Elementare Beispiele möglichst konformen Abbildungen im dreidimensionalen Raum, Wiss. Z. Martin-Luther-Univ. Halle-Wittenberg Math.-Natur. Reihe 11 (1962), 729–732.

    MathSciNet  MATH  Google Scholar 

  12. Nevanlinna, R. A remark on differentiable mappings, Michigan Math. J. 3 (1955/56), 53–57.

    Article  MathSciNet  Google Scholar 

  13. Nevanlinna, R. On differentiable mappings, Analytic Functions, ed. by L. Ahlfors et al., Princeton University Press, 3–9 (1960).

    Google Scholar 

  14. Reshetnyak, Ju. G. On conformal mappings of a space, Soviet Math. Dokl. 1(1960), 153–155.

    MathSciNet  MATH  Google Scholar 

  15. Rushing, T.B. Topological embeddings, Academic Press, 1973.

    MATH  Google Scholar 

  16. Semmes, S. On a question of Heinonen concerning the absolute continuity of quasisymmetric mappings, Rev. Mat. Iberoamericana. To appear.

    Google Scholar 

  17. Tukia, P., Väisälä, J. Quasisymmetric embeddings of metric spaces, Ann. Acad. Sci. Fenn. Ser. A I Math. 5 (1980), 97–114.

    MathSciNet  MATH  Google Scholar 

  18. Väisälä, J. Free quasiconformality in Banach spaces I, Ann. Acad. Sci. Fenn. Ser. A I Math. 15(1990), 355–379.

    MathSciNet  MATH  Google Scholar 

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Author information

Authors and Affiliations

  1. Matematiikan laitos, Helsingin yliopisto, Helsinki, Finland

    Jussi Väisälä

Authors
  1. Jussi Väisälä
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Editor information

Editors and Affiliations

  1. Department of Mathematics, University of Michigan, 4074 East Hall, Ann Arbor, MI, 48109-1109, USA

    Peter Duren

  2. Department of Mathematics, University of Michigan, 525 East University Street-East Hall, Ann Arbor, MI, 48109-1109, USA

    Juha Heinonen

  3. Department of Mathematics, Stanford University, Stanford, CA, 94305-2125, USA

    Brad Osgood

  4. Department of Mathematics, University of Texas, Austin, TX, 78712-1082, USA

    Bruce Palka

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© 1998 Springer Science+Business Media New York

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Väisälä, J. (1998). Questions on Quasiconformal Maps in Space. In: Duren, P., Heinonen, J., Osgood, B., Palka, B. (eds) Quasiconformal Mappings and Analysis. Springer, New York, NY. https://doi.org/10.1007/978-1-4612-0605-7_21

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  • DOI: https://doi.org/10.1007/978-1-4612-0605-7_21

  • Publisher Name: Springer, New York, NY

  • Print ISBN: 978-1-4612-6836-9

  • Online ISBN: 978-1-4612-0605-7

  • eBook Packages: Springer Book Archive

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