Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

Journals Home Search My Subscriptions Subscribe
Previous issue | This issue | Most recent issue | All issues (1950–Present) | Next issue | Previous article | Articles in press | Recently published articles | Next article
Request Permissions
 
 

 

Mappings of finite distortion: Removable singularities for locally homeomorphic mappings


Author: Kai Rajala
Journal: Proc. Amer. Math. Soc. 132 (2004), 3251-3258
MSC (2000): Primary 30C65
DOI: https://doi.org/10.1090/S0002-9939-04-07459-3
Published electronically: May 12, 2004
MathSciNet review: 2073299
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: Let $f$ be a locally homeomorphic mapping of finite distortion in dimension larger than two. We show that when the distortion of $f$satisfies a certain subexponential integrability condition, small sets are removable. The smallness is measured by a weighted modulus.

References [Enhancements On Off] (What's this?)

  • 1. S. Agard and A. Marden: A removable singularity theorem for local homeomorphisms, Indiana Univ. Math. J., 20 (1970), 455-461. MR 43:2209
  • 2. N. S. Dairbekov: Removable singularities of locally quasiconformal mappings, Siberian Math. J., 33 (1992), no. 1, 159-161. MR 93d:30029
  • 3. T. Iwaniec, P. Koskela, G. Martin, and C. Sbordone: Mappings of finite distortion: $L^n \log^{\chi} L$-integrability, J. London Math. Soc. (2), 67 (2003), no. 1, 123-136. MR 2003h:30031
  • 4. T. Iwaniec, P. Koskela, and J. Onninen: Mappings of finite distortion: Monotonicity and continuity, Invent. Math. 44 (2001), no. 3, 507-531. MR 2002c:30029
  • 5. T. Iwaniec, P. Koskela, and J. Onninen: Mappings of finite distortion: Compactness, Ann. Acad. Sci. Fenn. Math., 27 (2002), no. 2, 391-417. MR 2004b:30045
  • 6. T. Iwaniec and G. Martin: Geometric Function Theory and Nonlinear Analysis, Oxford Mathematical Monographs, The Clarendon Press, Oxford University Press, New York, 2001. MR 2003c:30001
  • 7. J. Kauhanen, P. Koskela, and J. Malý: Mappings of finite distortion: Discreteness and openness, Arch. Rational Mech. Anal., 160 (2001), 135-151. MR 2002m:30023
  • 8. J. Kauhanen, P. Koskela, and J. Malý: Mappings of finite distortion: Condition N, Michigan Math. J., 49 (2001), no. 1, 169-181. MR 2002d:30027
  • 9. J. Kauhanen, P. Koskela, J. Malý, J. Onninen, and X. Zhong: Mappings of finite distortion: Sharp Orlicz-conditions, Preprint 239, Department of Mathematics and Statistics, University of Jyväskylä, 2001.
  • 10. P. Koskela and J. Onninen: Mappings of finite distortion: Capacity and modulus inequalities, Preprint 257, Department of Mathematics and Statistics, University of Jyväskylä, 2002.
  • 11. P. Koskela and K. Rajala: Mappings of finite distortion: Removable singularities, Israel J. Math., 136 (2003), 269-283.
  • 12. J. Malý: Lectures on change of variables in integral, Graduate School in Helsinki, 2001.
  • 13. O. Martio, S. Rickman, and J. Väisälä: Distortion and singularities of quasiregular mappings, Ann. Acad. Sci. Fenn. Ser. A I Math., 465 (1970), 1-13. MR 42:1995
  • 14. O. Martio, S. Rickman, and J. Väisälä: Topological and metric properties of quasiregular mappings, Ann. Acad. Sci. Fenn. Ser. A I Math., 488 (1971), 1-31. MR 45:8830
  • 15. Yu. G. Reshetnyak: Space Mappings with Bounded Distortion, Transl. of Mathematical Monographs, vol. 73, Amer. Math. Soc., Providence, RI, 1989. MR 90d:30067
  • 16. S. Rickman: Quasiregular mappings, Ergebnisse der Mathematik und ihrer Grenzgebiete (3) [Results in Mathematics and Related Areas (3)], 26, Springer-Verlag, Berlin, 1993. MR 95g:30026
  • 17. J. Väisälä: Lectures on $n$-dimensional quasiconformal mappings, Springer-Verlag, Berlin and New York, 1971. MR 56:12260
  • 18. V. A. Zorich: Isolated singularity of mappings with bounded distortion, Mat. Sb., 81 (123) (1970), no. 4, 634-636; English transl., Math USSR-Sb., 10 (1970), 581-583. MR 42:497

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC (2000): 30C65

Retrieve articles in all journals with MSC (2000): 30C65

Additional Information

Kai Rajala
Affiliation: University of Jyväskylä, Department of Mathematics and Statistics, P.O. Box 35, FIN-40014 University of Jyväskylä, Finland
Email: kirajala@maths.jyu.fi

DOI: https://doi.org/10.1090/S0002-9939-04-07459-3
Received by editor(s): February 12, 2003
Received by editor(s) in revised form: July 2, 2003
Published electronically: May 12, 2004
Additional Notes: The author was supported by the foundations Magnus Ehrnroothin Säätiö and Vilho, Yrjö ja Kalle Väisälän Rahasto. A part of this research was done when the author was visiting at the University of Michigan. He wishes to thank the department for its hospitality.
Communicated by: Juha M. Heinonen
Article copyright: © Copyright 2004 American Mathematical Society