Distortion function and quasisymmetric mappings

J. Zając

Annales Polonici Mathematici (1991)

  • Volume: 55, Issue: 1, page 361-369
  • ISSN: 0066-2216

Abstract

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We study the relationship between the distortion function Φ K and normalized quasisymmetric mappings. This is part of a new method for solving the boundary values problem for an arbitrary K-quasiconformal automorphism of a generalized disc on the extended complex plane.

How to cite

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J. Zając. "Distortion function and quasisymmetric mappings." Annales Polonici Mathematici 55.1 (1991): 361-369. <http://eudml.org/doc/262398>.

@article{J1991,
abstract = {We study the relationship between the distortion function $Φ_K$ and normalized quasisymmetric mappings. This is part of a new method for solving the boundary values problem for an arbitrary K-quasiconformal automorphism of a generalized disc on the extended complex plane.},
author = {J. Zając},
journal = {Annales Polonici Mathematici},
keywords = {quasisymmetric mappings; distortion function},
language = {eng},
number = {1},
pages = {361-369},
title = {Distortion function and quasisymmetric mappings},
url = {http://eudml.org/doc/262398},
volume = {55},
year = {1991},
}

TY - JOUR
AU - J. Zając
TI - Distortion function and quasisymmetric mappings
JO - Annales Polonici Mathematici
PY - 1991
VL - 55
IS - 1
SP - 361
EP - 369
AB - We study the relationship between the distortion function $Φ_K$ and normalized quasisymmetric mappings. This is part of a new method for solving the boundary values problem for an arbitrary K-quasiconformal automorphism of a generalized disc on the extended complex plane.
LA - eng
KW - quasisymmetric mappings; distortion function
UR - http://eudml.org/doc/262398
ER -

References

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  1. [AVV1] G. D. Anderson, M. K. Vamanamurphy and M. Vuorinen, Distortion function for plane quasiconformal mappings, Israel J. Math. 62 (1) (1988), 1-16. 
  2. [AVV2] G. D. Anderson, M. K. Vamanamurphy and M. Vuorinen, Functional inequalities for hypergeometric and related functions, Univ. of Auckland, Rep. Ser. 242, 1990. 
  3. [BA] A. Beurling and L. V. Ahlfors, The boundary correspondence under quasiconformal mappings, Acta Math. 96 (1956), 125-142. Zbl0072.29602
  4. [HP] J. Hersch et A. Pfluger, Généralisation du lemme de Schwarz et du principe de la mesure harmonique pour les fonctions pseudo-analytiques, C. R. Acad. Sci. Paris 234 (1952), 43-45. Zbl0049.06304
  5. [H] O. Hübner, Remarks on a paper by Ławrynowicz on quasiconformal mappings, Bull. Acad. Polon. Sci. 18 (1980), 183-186. Zbl0195.36501
  6. [Ke] J. A. Kelingos, Boundary correspondence under quasiconformal mappings, Michigan Math. J. 13 (1966), 235-249. Zbl0146.30702
  7. [Kr1] J. G. Krzyż, Quasicircles and harmonic measure, Ann. Acad. Sci. Fenn. 12 (1987), 19-24. Zbl0563.30016
  8. [Kr2] J. G. Krzyż, Harmonic analysis and boundary correspondence under quasiconformal mappings, ibid. 14 (1989), 225-242. Zbl0663.30014
  9. [LV] O. Lehto and K. I. Virtanen, Quasiconformal Mappings in the Plane, 2nd ed., Grundlehren Math. Wiss. 126, Springer, New York 1973. Zbl0267.30016
  10. [W] C.-F. Wang, On the precision of Mori's theorem in Q-mappings, Science Record 4 (1960), 329-333. Zbl0103.30202
  11. [Z] J. Zając, The distortion function Φ K and quasihomographies, in: Space Quasiconformal Mappings, A collection of surveys 1960-1990, Springer, to appear 

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