Acta Mathematica

Area distortion of quasiconformal mappings

Kari Astala

Full-text: Open access

Article information

Acta Math. Volume 173, Number 1 (1994), 37-60.

Received: 8 February 1993
First available in Project Euclid: 31 January 2017

Permanent link to this document

Digital Object Identifier

Zentralblatt MATH identifier

1994 © Almqvist & Wiksell


Astala, Kari. Area distortion of quasiconformal mappings. Acta Math. 173 (1994), no. 1, 37--60. doi:10.1007/BF02392568.

Export citation


  • [A] Ahlfors, L., On quasiconformal mappings. J. Analyse Math., 3 (1954), 1–58.
  • [AB] Ahlfors, L. & Bers, L., Riemann's mapping theorem for variable metrics. Ann. of Math., 72, (1960), 385–404.
  • [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.
  • [BP] Becker, J. & Pommerenke, Chr., On the Hausdorff dimension of quasicircles. Ann. Acad., Sci. Fenn. Ser. A I Math., 12 (1987), 329–333.
  • [Bw] Bowen, R., Equilibrium States and the Ergodic Theory of Anosov Diffeomorphisms. Lecture Notes in Math., 470. Springer-Verlag, New York-Heidelberg, 1975.
  • [DH] Douady, A. & Hubbard, J., On the dynamics of polynomial-like mappings. Ann. Sci. École Norm. Sup., 18 (1985), 287–345.
  • [Ga] Garnett, J., Analytic Capacity and Measure. Lecture Notes in Math., 297. Springer-Verlag, New York-Heidelberg, 1972.
  • [Ge] Gehring, F. W., Open problems, in Proc. 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.
  • [GV] Gehring, F. W. & Väisälä, J., Hausdorff dimension and quasiconformal mappings. J. London Math. Soc. (2), 6 (1975), 504–512.
  • [H] Hutchinson, J. E., Fractals and self-similarity. Indiana Univ. Math. J., 30 (1981), 713–747.
  • [I] Iwaniec, T., Lp-theory of quasiregular mappings, in Quasiconformal Space Mappings, A Collection of Surveys 1960–1990. Lecture Notes in Math., 1508, pp. 39–64. Springer-Verlag, New York-Heidelberg, 1992.
  • [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.
  • [IM2]— Quasiconformal mappings and capacity. Indiana Univ. Math. J., 40 (1991), 101–122.
  • [JM] Jones, P. & Makarov, N., Density properties of harmonic measure. To appear in Ann. of Math.
  • [JV] Järvi, P. & Vuorinen, M., Self-similar Cantor sets and quasiregular mappings. J. Reine Angew. Math., 424 (1992), 31–45.
  • [K] Koskela, P., The degree of regularity of a quasiconformal mapping. To appear in Proc. Amer. Math. Soc.
  • [KM] Koskela, P. & Martio, O., Removability theorems for quasiregular mappings. To appear in Ann. Acad. Sci. Fenn. Ser. A I Math.
  • [L] Lehto, O., Univalent Functions and Teichmüller Spaces. Springer-Verlag, New York-Heidelberg, 1987.
  • [LV] Lehto, O. & Virtanen K., Quasiconformal Mappings in the Plane. Second edition. Springer-Verlag, New York-Heidelberg, 1973.
  • [Ma] Manning, A., The dimension of the maximal measure for, a polynomial map. Ann. of Math., 119 (1984), 425–430.
  • [Mo] Mori, A., On an absolute constant in the theory of quasiconformal mappings. J. Math. Soc. Japan, 8 (1956), 156–166.
  • [MSS] Mañé, R., Sad, P. & Sullivan, D., On the dynamics of rational maps. Ann. Sci. École Norm. Sup., 16 (1983), 193–217.
  • [P] Pommerenke, Chr., Univalent Functions. Vandenhoeck & Ruprecht, Göttingen 1975.
  • [Ri] Rickman, S., Nonremovable Cantor sets for bounded quasiregular mappings. To appear in Ann. Acad. Sci. Fenn. Ser A I Math.
  • [Ru] Ruelle, D., Repellers for real analytic maps. Ergodic Theory Dynamical Systems, 2 (1982), 99–107.
  • [Sl] Slodkowski, Z., Holomorphic motions, and polynomial hulls. Proc. Amer. Math. Soc., 111 (1991), 347–355.
  • [Su] Sullivan, D., Quasiconformal homeomorphisms and dynamics I, II. Ann. of Math., 122 (1985), 401–418; Acta Math., 155 (1985), 243–260.
  • [W] Walters, P., An Introduction to Ergodic Theory. Springer-Verlag, New York-Heidelberg, 1982.