Skip to main content
SpringerLink
Log in

Quasiregular mappings in even dimensions

  • Published:
Acta Mathematica

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

References

  1. Ahlfors, L. V.,Lectures on Quasiconformal Mappings. Van Nostrand, Princeton, 1966; Reprinted by Wadsworth Inc., Belmont, 1987.

    Google Scholar 

  2. —, Conditions for quasiconformal deformations in several variables, inContributions to Analysis, pp. 19–25. Academic Press, New York, 1974.

    Google Scholar 

  3. Ahlfors, L. V. &Beurling, A., Conformal invariants and function theoretic null sets.Acta Math., 83 (1950), 101–129.

    MathSciNet  Google Scholar 

  4. Boyarski, B. V., Homeomorphic solutions of Beltrami systems.Dokl. Akad. Nauk SSSR, 102 (1955), 661–664.

    MathSciNet  Google Scholar 

  5. Boyarski, B. V. &Iwaniec, T., Another approach to Liouville Theorem.Math. Nachr., 107 (1982), 253–262.

    MathSciNet  Google Scholar 

  6. —, Analytical foundations of the theory of quasiconformal mappings in Rn.Ann. Acad. Sci. Fenn. Ser. A I Math., 8 (1983), 257–324.

    MathSciNet  Google Scholar 

  7. Donaldson, S. K. &Sullivan, D. P., Quasiconformal 4-manifolds.Acta Math., 163 (1989), 181–252.

    MathSciNet  Google Scholar 

  8. Edwards, R. E.,Fourier Series, vol. II. Holt, Rinehart, Winston, 1967.

    Google Scholar 

  9. Fifiel, T., Iwaniec, T. &Pelczynski, A., Computing norms and critical exponents of some operators inL p-spaces.Studia Math., 79 (1984), 227–274.

    MathSciNet  Google Scholar 

  10. Flanders, H.,Differential Forms. Academic Press, 1963.

  11. Freed, D. S. & Uhlenbeck, K. K.,Instantons and Four Manifolds. Math. Sci. Res. Publ., 1. Springer-Verlag, 1972.

  12. Garnett, J.,Analytic Capacity and Measure. Lecture Notes in Math., 297. Springer-Verlag, 1972.

  13. Garcia-Cuerva, J. & Rubio de Francia, J. L.,Weighted Norm Inequalities and Related Topics. Notas de Matemática, 104; North-Holland Math. Studies, 116. North-Holland, 1985.

  14. Gehring, F. W., Rings and quasiconformal mappings in space.Trans. Amer. Math. Soc., 103 (1962), 353–393.

    Article  MATH  MathSciNet  Google Scholar 

  15. —, TheL p-integrability of the partial derivatives of a quasiconformal mapping.Acta Math., 130 (1973), 265–277.

    MATH  MathSciNet  Google Scholar 

  16. Gehring, F. W., Topics in quasiconformal mappings, inProceedings of the ICM, Berkeley, 1986, pp. 62–82.

  17. Granlund, S., Lindqvist, P. &Martio, O., Conformally invariant variational integrals.Trans. Amer. Math. Soc., 277 (1983), 43–73.

    Article  MathSciNet  Google Scholar 

  18. Iwaniec, T., Some aspects of partial differential equations and quasiregular mappings, inProceedings of the ICM, Warsaw, 1983, pp. 1193–1208.

  19. Iwaniec, T.,Regularity Theorems for the Solutions of Partial Differential Equations Related to Quasiregular Mappings in Several Variables. Preprint Polish Acad. Sci., Habilitation Thesis, pp. 1–45, 1978; Dissertationes Mathematicae, CXCVIII, 1982.

  20. Iwaniec, T., On Cauchy-Riemann derivatives in several real variables.Lecture Notes in Math., 1039 (1983), 220–224. Springer-Verlag.

  21. —, Projections onto gradient fields andL p-estimates for degenerate elliptic operators.Studia Math., 75 (1983), 293–312.

    MathSciNet  Google Scholar 

  22. —,p-harmonic tensors and quasiregular mappings.Ann. of Math., 136 (1992), 651–685.

    Article  MathSciNet  Google Scholar 

  23. Iwaniec, T. &Martin, G. J., Quasiconformal mappings and capacity.Indiana Math. J., 40 (1991), 101–122.

    Article  MathSciNet  Google Scholar 

  24. Iwaniec, T. & Martin, G. J., The Beurling-Ahlfors transform in Rn and related singular integrals. I.H.E.S. Preprint, 1990.

  25. Järvi, P. & Vuorinen, M., Self-similar Cantor sets and quasiregular mappings. Institut Mittag-Leffler Report, no. 27, 1989/90; To appear inJ. Reine Angew. Math.

  26. Koskela, P. & Martio, O., Removability theorems for quasiregular mappings. To appear inAnn. Acad. Sci. Fenn. Ser. A I Math.

  27. Lawson, H. B. & Michelson, M. L.,Spin Geometry. Princeton Univ. Press, 1989.

  28. Lehto, O., Quasiconformal mappings and singular integrals.Sympos. Math., XVIII (1976), 429–453. Academic Press, London.

    Google Scholar 

  29. Lelong-Ferrand, J., Geometrical interpretations of scalar curvature and regularity of conformal homeomorphisms, inDifferential Geometry and Relativity (A. Lichnerowicz Sixtieth Birthday Volume), Reidel, 1976, pp. 91–105.

  30. Liouville, J., Théorème sur l'équationdx 2+dy 2+dz 2 = λ(dα 2+dβ 2+dγ 2).J. Math. Pures Appl. 1, 15 (1850), 103.

    Google Scholar 

  31. Manfredi, J., Regularity for minima of functionals withp-growth.J. Differential Equations, 76 (1988), 203–212.

    Article  MATH  MathSciNet  Google Scholar 

  32. Maz'ja, G. V.,Sobolev Spaces. Springer-Verlag, 1985.

  33. Martio, O., Rickman, S. &Väisälä, J., Definitions for quasiregular mappings.Ann. Acad. Sci. Fenn. Ser. AI Math., 448 (1969), 1–40.

    Google Scholar 

  34. —, Distortion and singularities of quasiregular mappings.Ann. Acad. Sci. Fenn. Ser. A I Math., 465 (1970), 1–13.

    Google Scholar 

  35. —, Topological and metric properties of quasiregular mappings.Ann. Acad. Sci. Fenn. Ser. A I Math., 488 (1971), 1–31.

    Google Scholar 

  36. Martio, O. &Sarvas, J., Injective theorems in plane and space.Ann. Acad. Sci. Fenn. Ser. A I Math., 4 (1979), 383–401.

    MathSciNet  Google Scholar 

  37. Martio, O. &Srebro, U., Automorphic quasimeromorphic mappings.Acta Math., 135 (1975), 221–247.

    MathSciNet  Google Scholar 

  38. Poletsky, E. A., On the removal of singularities of quasiconformal mappings.Math. USSSR-Sb., 21 (1973), 240–254.

    Article  Google Scholar 

  39. Peltonen, K.,Quasiregular Mappings onto S n. Lic. Thesis, Helsinki, 1988.

  40. Reshetnyak, Y. G., Liouville's conformal mapping theorem under minimal regularity assumptions.Sibirsk. Mat. Zh., 8 (1967), 835–840.

    MATH  Google Scholar 

  41. —, Differentiable properties of quasiconformal mappings and conformal mappings of Riemannian spaces.Sibirsk. Mat. Zh., 19 (1978), 1166–1183.

    MATH  MathSciNet  Google Scholar 

  42. —Space Mappings with Bounded Distortion. Transl. Math. Monographs, 73, Amer. Math. Soc., Providence, 1989.

    Google Scholar 

  43. Rickman, S., The analogue of Picard's Theorem for quasiregular mappings in dimension three.Acta Math., 154 (1985), 195–242.

    MATH  MathSciNet  Google Scholar 

  44. —, Asymptotic values and angular limits of quasiregular mappings of a ball.Ann. Acad. Sci. Fenn. Ser. A I Math., 5 (1980), 185–196.

    MATH  MathSciNet  Google Scholar 

  45. Rickman, S., Nonremovable Cantor sets for bounded quasiregular mappings. To appear inAnn. Acad. Sci. Fenn. Ser. A I Math.

  46. Rickman, S., Quasiregular mappings. To appear.

  47. Sarvas, J., Quasiconformal semiflows.Ann. Acad. Sci. Fenn. Ser. A I Math. 7 (1982), 197–219.

    MATH  MathSciNet  Google Scholar 

  48. Stein, E. M.,Singular Integrals and Differentiable Properties of Functions. Princeton Univ. Press, 1970.

  49. Teleman, N., The Index Theorem for topological manifolds.Acta Math., 153 (1984), 117–152.

    MATH  MathSciNet  Google Scholar 

  50. Tukia, P., Hausdorff dimension and quasisymmetric mappings.Math. Scand., 65 (1989), 152–160.

    MATH  MathSciNet  Google Scholar 

  51. —, Automorphic quasimeromorphic mappings for torisonless hyperbolic groups.Ann. Acad. Sci. Fenn. Ser. A I Math., 10 (1985), 545–560.

    MATH  MathSciNet  Google Scholar 

  52. Vuorinen, M.,Conformal Geometry and Quasiregular Mappings. Lecture Notes in Math., 1319. Springer-Verlag, 1988.

Download references

Author information

Authors and Affiliations

  1. Institut Mittag-Leffler, Djursholm, Sweden

    Tadeusz Iwaniec & Gaven Martin

  2. Department of Mathematics, Syracuse University, 13244, Syracuse, New York, USA

    Tadeusz Iwaniec

  3. Department of Mathematics and Statistics, University of Auckland, Auckland, New Zealand

    Gaven Martin

Authors
  1. Tadeusz Iwaniec
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Gaven Martin
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

Research supported in part by a grant from the U.S. National Science Foundation, DMS-9007946

Rights and permissions

Reprints and permissions

About this article

Cite this article

Iwaniec, T., Martin, G. Quasiregular mappings in even dimensions. Acta Math. 170, 29–81 (1993). https://doi.org/10.1007/BF02392454

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02392454

Keywords

Search

Navigation