Skip to main content
SpringerLink
Log in

Mappings of finite distortion: Removable singularities

  • Published:
Israel Journal of Mathematics Aims and scope Submit manuscript

Abstract

We show that certain small sets are removable for bounded mappings of finite distortion for which the distortion function satisfies a suitable subexponential integrability condition. We also give an example demonstrating the sharpness of this condition.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. K. Astala, T. Iwaniec, P. Koskela and G. Martin,Mappings of BMO-bounded distortion, Mathematische Annalen317 (2000), 703–726.

    Article  MATH  MathSciNet  Google Scholar 

  2. T. Iwaniec, P. Koskela and G. Martin,Mappings of BMO-distortion and Beltramitype operators, Journal d’Analyse Mathématique88 (2002), 337–381.

    MATH  MathSciNet  Google Scholar 

  3. T. Iwaniec, P. Koskela, G. Martin and C. Sbordone,Mappings of finite distortion: L n logα L-integrability, Journal of the London Mathematical Society (2)67 (2003), 123–136.

    Article  MATH  MathSciNet  Google Scholar 

  4. T. Iwaniec, P. Koskela and J. Onninen,Mappings of finite distortion: Monotonicity and continuity, Inventiones Mathematicae44 (2001), 507–531.

    Article  MathSciNet  Google Scholar 

  5. T. Iwaniec, P. Koskela and J. Onninen,Mappings of finite distortion: Compactness, Annales Academiae Scientiarum Fennicae. Mathematica27 (2002), 391–417.

    MATH  MathSciNet  Google Scholar 

  6. T. Iwaniec and G. Martin,Quasiregular mappings in even dimensions, Acta Mathematica170 (1993), 29–81.

    Article  MATH  MathSciNet  Google Scholar 

  7. T. Iwaniec and G. Martin,The Beltrami equation, Memoirs of the American Mathematical Society, to appear.

  8. T. Iwaniec and G. J. Martin,Geometric Function Theory and Nonlinear Analysis, Oxford Mathematical Monographs, Oxford University Press, 2001.

  9. J. Kauhanen, P. Koskela and J. Malý,On functions with derivatives in a Lorentz space, Manuscripta Mathematica100 (1999), 87–101.

    Article  MATH  MathSciNet  Google Scholar 

  10. J. Kauhanen, P. Koskela and J. Malý,Mappings of finite distortion: Discreteness and openness, Archive for Rational Mechanics and Analysis160 (2001), 135–151.

    Article  MATH  MathSciNet  Google Scholar 

  11. J. Kauhanen, P. Koskela and J. Malý,Mappings of finite distortion: Condition N, The Michigan Mathematical Journal9 (2001), 169–181.

    Article  Google Scholar 

  12. J. Kauhanen, P. Koskela, J. Malý, J. Onninen and X. Zhong,Mappings of finite distortion: Sharp Orlicz-conditions, Revista Matematica Iberoamericana, to appear; Preprint 239, Department of Mathematics and Statistics, University of Jyväskylä, 2001.

  13. Yu. G. Reshetnyak,Space Mappings with Bounded Distortion, Translations of Mathematical Monographs, Vol. 73, American Mathematical Society, Providence, RI, 1989.

    MATH  Google Scholar 

  14. S. Rickman,Quasiregular mappings, Ergebnisse der Mathematik und ihrer Grenzgebiete (3) [Results in Mathematics and Related Areas (3)], 26, Springer-Verlag, Berlin, 1993.

    MATH  Google Scholar 

  15. V. Ryazanov, U. Srebro and E. Yakubov,BMO-quasiconformal mappings, Journal d’Analyse Mathématique83 (2001), 1–20.

    MATH  MathSciNet  Google Scholar 

  16. M. Vuorinen,Conformal geometry and quasiregular mappings, Lecture Notes in Mathematics1319, Springer-Verlag, Berlin, 1988.

    MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics and Statistics, University of Jyväskylä, P.O. Box 35, FIN-40351, Jyväskylä, Finland

    Pekka Koskela & Kai Rajala

Authors
  1. Pekka Koskela
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Kai Rajala
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Pekka Koskela.

Additional information

Both authors were supported in part by the Academy of Finland, project 39788. K.R. was also supported by the foundation Magnus Ehrnroothin Säätiö. This research was done when the authors were visiting at the University of Michigan, P.K. as the Fred and Lois Gehring professor. They wish to thank the institute for the hospitality.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Koskela, P., Rajala, K. Mappings of finite distortion: Removable singularities. Isr. J. Math. 136, 269–283 (2003). https://doi.org/10.1007/BF02807201

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02807201

Keywords

Search

Navigation