Arkiv för Matematik

  • Ark. Mat.
  • Volume 18, Number 1-2 (1980), 157-180.

On the existence of angular limits of n-dimensional quasiconformal mappings

Matti Vuorinen

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Article information

Source
Ark. Mat., Volume 18, Number 1-2 (1980), 157-180.

Dates
Received: 18 April 1979
First available in Project Euclid: 31 January 2017

Permanent link to this document
https://projecteuclid.org/euclid.afm/1485896615

Digital Object Identifier
doi:10.1007/BF02384688

Mathematical Reviews number (MathSciNet)
MR608334

Zentralblatt MATH identifier
0461.30014

Rights
1980 © Institut Mittag-Leffler

Citation

Vuorinen, Matti. On the existence of angular limits of n -dimensional quasiconformal mappings. Ark. Mat. 18 (1980), no. 1-2, 157--180. doi:10.1007/BF02384688. https://projecteuclid.org/euclid.afm/1485896615


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References

  • Bagemihl, F. and Seidel, W., Sequential and continuous limits of meromorphic functions, Ann. Acad. Sci Fenn. Ser. A. I 280 (1960), 1–17.
  • Doob, J. L., The boundary values of analytic functions, Trans. Amer. Math. Soc. 34 (1932), 153–170.
  • Gehring, F. W., The Carathéodory convergence theorem for quasiconformal mappings in space, Ann. Acad. Sci. Fenn. Ser. A I 336/11 (1963), 1–21.
  • Gehring, F. W., A remark on domains quasiconformally equivalent to a ball, Ann. Acad. Sci. Fenn. Ser. A. I 2 (1976), 147–155.
  • Hall, T., Sur la mesure harmonique de certains ensembles Ark. Mat. Astr., Fys. 25A, No. 28 (1937), 1–8.
  • Lehto, O. and Virtanen, K. I., Boundary behaviour and normal meromorphic functions, Acta Math. 97 (1957), 47–65.
  • Martio, O., Rickman, S. and Väisälä, J., Definitions for quasiregular mappings, Ann. Acad. Sci. Fenn. Ser. A I 448 (1969), 1–40.
  • Martio, O., Rickman, S. and Väisälä, J., Distortion and singularities of quasiregular mappings, Ann. Acad. Sci. Fenn. Ser. A I 465 (1970), 1–13.
  • Martio, O. and Sarvas, J., Density conditions in the n-capacity, Indiana Univ. Math. J. 26 (1977), 761–776.
  • Mićić, V. P., A theorem of Lindelöf type for quasiconformal mappings in space, Mat. Vesnik 9 (24) (1972), 3–8.
  • Näkki, R., Extension of Loewner’s capacity theorem, Trans. Amer. Math. Soc. 180, (1973), 229–236.
  • Näkki, R., Prime ends and quasiconformal mappings, J. Analyse Math. 35 (1979), 13–40.
  • Sarvas, J., Symmetrization of condensers in n-space, Ann. Acad. Sci. Fenn. Ser. A I 522 (1972), 1–44.
  • Väisälä, J., Lectures on n-dimensional quasiconformal mappings, Lecture Notes in Mathematics 229, Springer-Verlag, Berlin-Heidelberg-New York, 1971.
  • Vuorinen, M., Exceptional sets and boundary behavior of quasiregular mappings in n-space, Ann. Acad. Sci. Fenn. Ser. A. I Math. Dissertationes 11 (1976), 1–44.
  • Vuorinen, M., On angular limits of closed quasiregular mappings. Proceedings of the First Finnish-Polish Summer School in Complex Analysis, Part II, Held at Podlesice, Poland, June 16–22, 1977), Edited by J. Ŀawrynowicz and O. Lehto, University of Ŀódź, Ŀódź 1978, 69–74.
  • Vuorinen, M., Capacity densities and angular limits of quasiregular mappings, Trans. Amer. Math. Soc. (to appear).
  • Wallin, H., Metrical characterization of conformal capacity zero, J. Math. Anal. Appl. 58 (1977), 298–311.
  • Ziemer, W. P., Extremal length and p-capacity, Michigan Math. J. 16 (1969), 43–51.