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Area distortion of quasiconformal mappings

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References

  • [A]Ahlfors, L., On quasiconformal mappings.J. Analyse Math., 3 (1954), 1–58.

    Article  MATH  MathSciNet  Google Scholar 

  • [AB]Ahlfors, L. &Bers, L., Riemann's mapping theorem for variable metrics.Ann. of Math., 72, (1960), 385–404.

    Article  MathSciNet  Google Scholar 

  • [AM]Astala, K. & Martin, G., Holomorphic motions. Preprint, 1992.

  • [Bj]Bojarski, B., Generalized solutions of a system of differential equations of first order and elliptic type with discontinuous coefficients.Math. Sb., 85 (1957), 451–503.

    MathSciNet  Google Scholar 

  • [BP]Becker, J. &Pommerenke, Chr., On the Hausdorff dimension of quasicircles.Ann. Acad., Sci. Fenn. Ser. A I Math., 12 (1987), 329–333.

    MathSciNet  MATH  Google Scholar 

  • [Bw]Bowen, R.,Equilibrium States and the Ergodic Theory of Anosov Diffeomorphisms. Lecture Notes in Math., 470. Springer-Verlag, New York-Heidelberg, 1975.

    MATH  Google Scholar 

  • [DH]Douady, A. &Hubbard, J., On the dynamics of polynomial-like mappings.Ann. Sci. École Norm. Sup., 18 (1985), 287–345.

    MathSciNet  MATH  Google Scholar 

  • [Ga]Garnett, J.,Analytic Capacity and Measure. Lecture Notes in Math., 297. Springer-Verlag, New York-Heidelberg, 1972.

    MATH  Google Scholar 

  • [Ge]Gehring, F. W., Open problems, inProc. Romanian-Finnish Seminar on Teichmüller Spaces and Quasiconformal Mappings, Braçov, 1969, p. 306.

  • [GR]Gehring, F. W. &Reich, E., Area distortion under quasiconformal mappings.Ann. Acad. Sci. Fenn. Ser. A I Math., 388 (1966), 1–14.

    MathSciNet  Google Scholar 

  • [GV]Gehring, F. W. &Väisälä, J., Hausdorff dimension and quasiconformal mappings.J. London Math. Soc. (2), 6 (1975), 504–512.

    Google Scholar 

  • [H]Hutchinson, J. E., Fractals and self-similarity.Indiana Univ. Math. J., 30 (1981), 713–747.

    Article  MATH  MathSciNet  Google Scholar 

  • [I]Iwaniec, T.,L p-theory of quasiregular mappings, inQuasiconformal Space Mappings, A Collection of Surveys 1960–1990. Lecture Notes in Math., 1508, pp. 39–64. Springer-Verlag, New York-Heidelberg, 1992.

    Google Scholar 

  • [IK]Iwaniec, T. & Kosecki, R., Sharp estimates for complex potentials and quasiconformal mappings. Preprint of Syracuse University.

  • [IM1]Iwaniec, T. &Martin, G., Quasiregular mappings in even dimensions.Acta Math., 170, (1992), 29–81.

    MathSciNet  Google Scholar 

  • [IM2]— Quasiconformal mappings and capacity.Indiana Univ. Math. J., 40 (1991), 101–122.

    Article  MATH  MathSciNet  Google Scholar 

  • [JM]Jones, P. & Makarov, N., Density properties of harmonic measure. To appear inAnn. of Math.

  • [JV]Järvi, P. &Vuorinen, M., Self-similar Cantor sets and quasiregular mappings.J. Reine Angew. Math., 424 (1992), 31–45.

    MathSciNet  MATH  Google Scholar 

  • [K]Koskela, P., The degree of regularity of a quasiconformal mapping. To appear inProc. Amer. Math. Soc.

  • [KM]Koskela, P. & Martio, O., Removability theorems for quasiregular mappings. To appear inAnn. Acad. Sci. Fenn. Ser. A I Math.

  • [L]Lehto, O.,Univalent Functions and Teichmüller Spaces. Springer-Verlag, New York-Heidelberg, 1987.

    MATH  Google Scholar 

  • [LV]Lehto, O. &Virtanen K.,Quasiconformal Mappings in the Plane. Second edition. Springer-Verlag, New York-Heidelberg, 1973.

    MATH  Google Scholar 

  • [Ma]Manning, A., The dimension of the maximal measure for, a polynomial map.Ann. of Math., 119 (1984), 425–430.

    Article  MATH  MathSciNet  Google Scholar 

  • [Mo]Mori, A., On an absolute constant in the theory of quasiconformal mappings.J. Math. Soc. Japan, 8 (1956), 156–166.

    Article  MATH  MathSciNet  Google Scholar 

  • [MSS]Mañé, R., Sad, P. &Sullivan, D., On the dynamics of rational maps.Ann. Sci. École Norm. Sup., 16 (1983), 193–217.

    MATH  Google Scholar 

  • [P]Pommerenke, Chr.,Univalent Functions. Vandenhoeck & Ruprecht, Göttingen 1975.

    MATH  Google Scholar 

  • [Ri]Rickman, S., Nonremovable Cantor sets for bounded quasiregular mappings. To appear inAnn. Acad. Sci. Fenn. Ser A I Math.

  • [Ru]Ruelle, D., Repellers for real analytic maps.Ergodic Theory Dynamical Systems, 2 (1982), 99–107.

    Article  MATH  MathSciNet  Google Scholar 

  • [Sl]Slodkowski, Z., Holomorphic motions, and polynomial hulls.Proc. Amer. Math. Soc., 111 (1991), 347–355.

    Article  MATH  MathSciNet  Google Scholar 

  • [Su]Sullivan, D., Quasiconformal homeomorphisms and dynamics I, II.Ann. of Math., 122 (1985), 401–418;Acta Math., 155 (1985), 243–260.

    Article  MATH  MathSciNet  Google Scholar 

  • [W]Walters, P.,An Introduction to Ergodic Theory. Springer-Verlag, New York-Heidelberg, 1982.

    MATH  Google Scholar 

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  1. Department of Mathematics, University of Helsinki, P.O. Box 4, SF-00014, Finland

    Kari Astala

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  1. Kari Astala
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Astala, K. Area distortion of quasiconformal mappings. Acta Math. 173, 37–60 (1994). https://doi.org/10.1007/BF02392568

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