Revista Matemática Iberoamericana

Mappings of finite distortion: Sharp Orlicz-conditions

Janne Kauhanen, Pekka Koskela, Jan Malý, Jani Onninen, and Xiao Zhong

Full-text: Open access

Abstract

We establish continuity, openness and discreteness, and the condition $(N)$ for mappings of finite distortion under minimal integrability assumptions on the distortion.

Article information

Source
Rev. Mat. Iberoamericana, Volume 19, Number 3 (2003), 857-872.

Dates
First available in Project Euclid: 20 February 2004

Permanent link to this document
https://projecteuclid.org/euclid.rmi/1077293808

Mathematical Reviews number (MathSciNet)
MR2053566

Zentralblatt MATH identifier
1059.30017

Subjects
Primary: 30C65: Quasiconformal mappings in $R^n$ , other generalizations

Keywords
Orlicz conditions finite distortion continuity openness and discreteness

Citation

Kauhanen, Janne; Koskela, Pekka; Malý, Jan; Onninen, Jani; Zhong, Xiao. Mappings of finite distortion: Sharp Orlicz-conditions. Rev. Mat. Iberoamericana 19 (2003), no. 3, 857--872. https://projecteuclid.org/euclid.rmi/1077293808


Export citation

References

  • Astala, K., Iwaniec, T., Koskela, P. and Martin, G.: Mappings of BMO-bounded distortion. Math. Ann. 317 (2000), no. 4, 703-726.
  • David, G.: Solutions de l'equation de Beltrami avec $||\mu||_\infty=1$. Ann. Acad. Sci. Fenn. Ser. A I, Math. 13 (1988), no. 1, 25-70.
  • Giannetti, F., Iwaniec, T., Onninen, J. and Verde, A.: Estimates of Jacobians by subdeterminants. J. Geom. Anal. 12 (2002), no. 2, 223-254.
  • Greco, L.: Sharp integrability of nonnegative Jacobians. Rend. Mat. Appl. (7) 18 (1998), no. 3, 585-600.
  • Iwaniec, T., Koskela P. and Martin, G.: Mappings of BMO-distortion and Beltrami type operators. J. Anal. Math. 88 (2002), 337-381.
  • Iwaniec, T., Koskela P. and Onninen, J.: Mappings of finite distortion: Monotonicity and continuity. Invent. Math. 144 (2001), no. 3, 507-531.
  • Iwaniec, T. and Martin, G.: The Beltrami equation. Mem. Amer. Math. Soc., to appear.
  • Iwaniec, T. and Martin, G.: Geometric function theory and non-linear analysis. Oxford Mathematical Monographs. The Clarendon Press, Oxford University Press, 2001.
  • Kauhanen, J., Koskela, P. and Malý, J.: Mappings of finite distortion: Discreteness and openness. Arch. Ration. Mech. Anal. 160 (2001), no. 2, 135-151.
  • Kauhanen, J., Koskela, P. and Malý, J.: Mappings of finite distortion: Condition N. Michigan Math. J. 49 (2001), no. 1, 169-181.
  • Koskela, P. and Zhong, X.: Minimal assumptions for the integrability of the Jacobian. Manuscript.
  • Manfredi, J. and Villamor, E.: An extension of Reshetnyak's theorem. Indiana Univ. Math. J. 47 (1998), no. 3, 1131-1145.
  • Reshetnyak, Yu. G.: Space Mappings with Bounded Distortion. Sibirsk. Mat. Z. 8 (1967), 629-658.
  • Reshetnyak, Yu. G.: Space Mappings with Bounded Distortion. Trans. of Mathematical Monographs 73. American Mathematical Society, 1989.
  • Rickman, S.: Quasiregular mappings. Ergebnisse der Mathematik und ihrer Grenzgebiete (3) [Results in Mathematics and Related Areas (3)] 26. Springer-Verlag, Berlin, 1993.