The Michigan Mathematical Journal

Metric definition of μ-homeomorphisms

Sari Kallunki and Pekka Koskela

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Michigan Math. J., Volume 51, Issue 1 (2003), 141-152.

First available in Project Euclid: 8 April 2003

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 30C65: Quasiconformal mappings in $R^n$ , other generalizations 30C62: Quasiconformal mappings in the plane


Kallunki, Sari; Koskela, Pekka. Metric definition of μ-homeomorphisms. Michigan Math. J. 51 (2003), no. 1, 141--152. doi:10.1307/mmj/1049832897.

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  • B. Bojarski, Remarks on Sobolev imbedding inequalities, Complex analysis (Joensuu 1987), Lecture Notes in Math., 1351, pp. 52--68, Springer-Verlag, Berlin, 1988.
  • G. David, Solutions de l'equation de Beltrami avec $\|\mu\|_\infty=1,$ Ann. Acad. Sci. Fenn. Ser. A I Math. 13 (1988), 25--70.
  • F. W. Gehring, Rings and quasiconformal mappings in space, Trans. Amer. Math. Soc. 103 (1962), 353--393.
  • J. Graczyk and S. Smirnov, Non-uniform hyperbolicity in complex dynamics I, II, preprint.
  • P. Haïssinsky, Chirurgie parabolique, C. R. Acad. Sci. Paris Sér. I Math. 327 (1998), 195--198.
  • ------, Chirurgie croisée, Bull. Soc. Math. France 128 (2000), 599--654.
  • J. Heinonen and P. Koskela, Definitions of quasiconformality, Invent. Math. 120 (1995), 61--79.
  • T. Iwaniec, P. Koskela, and G. Martin, Mappings of BMO-distortion and Beltrami type operators, J. Anal. Math. (to appear).
  • T. Iwaniec, P. Koskela, G. Martin, and C. Sbordone, Mappings of finite distortion: $L^n\,\text\rm log\,L$-integrability, J. London Math. Soc. (2) (to appear).
  • S. Kallunki, Mappings of finite distortion: The metric definition, Ann. Acad. Sci. Fenn. Math. Diss. 131 (2002), 1--33.
  • S. Kallunki and P. Koskela, Exceptional sets for the definition of quasiconformality, Amer. J. Math. 122 (2000), 735--743.
  • S. Kallunki and O. Martio, ACL homeomorphisms and linear dilatation, Proc. Amer. Math. Soc. 130 (2002), 1073--1078.
  • J. Kauhanen, P. Koskela, and J. Malý, Mappings of finite distortion: Condition $N,$ Michigan Math. J. 49 (2001), 169--181.
  • P. Koskela and J. Malý, Mappings of finite distortion: The zero set of the Jacobian, J. Eur. Math. Soc. (to appear).
  • P. Mattila, Geometry of sets and measures in Euclidean spaces. Fractals and rectifiability, Cambridge Stud. Adv. Math., 44, Cambridge Univ. Press, Cambridge, U.K., 1995.
  • T. Rado and P. V. Reichelderfer, Continuous transformations in analysis, Springer-Verlag, Berlin, 1955.
  • V. Ryazanov, U. Srebro, and E. Yakubov, BMO-quasiconformal mappings, J. Anal. Math. 83 (2001), 1--20.
  • P. Tukia, Compactness properties of $\mu$-homeomorphisms, Ann. Acad. Sci. Fenn. Ser. A I Math. 16 (1991), 47--69.
  • J. Väisälä, Lectures on $n$-dimensional quasiconformal mappings, Lecture Notes in Math., 229, Springer-Verlag, Berlin, 1971.