Sufficient conditions for quasiconformality of harmonic mappings of the upper halfplane onto itself

Andrzej Michalski

Annales UMCS, Mathematica (2008)

  • Volume: 62, Issue: 1, page 91-104
  • ISSN: 2083-7402

Abstract

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In this paper we introduce a class of increasing homeomorphic self-mappings of R. We define a harmonic extension of such functions to the upper halfplane by means of the Poisson integral. Our main results give some sufficient conditions for quasiconformality of the extension.

How to cite

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Andrzej Michalski. "Sufficient conditions for quasiconformality of harmonic mappings of the upper halfplane onto itself." Annales UMCS, Mathematica 62.1 (2008): 91-104. <http://eudml.org/doc/268030>.

@article{AndrzejMichalski2008,
abstract = {In this paper we introduce a class of increasing homeomorphic self-mappings of R. We define a harmonic extension of such functions to the upper halfplane by means of the Poisson integral. Our main results give some sufficient conditions for quasiconformality of the extension.},
author = {Andrzej Michalski},
journal = {Annales UMCS, Mathematica},
keywords = {Harmonic mappings; Poisson integral; quasiconformal mappings; harmonic mappings},
language = {eng},
number = {1},
pages = {91-104},
title = {Sufficient conditions for quasiconformality of harmonic mappings of the upper halfplane onto itself},
url = {http://eudml.org/doc/268030},
volume = {62},
year = {2008},
}

TY - JOUR
AU - Andrzej Michalski
TI - Sufficient conditions for quasiconformality of harmonic mappings of the upper halfplane onto itself
JO - Annales UMCS, Mathematica
PY - 2008
VL - 62
IS - 1
SP - 91
EP - 104
AB - In this paper we introduce a class of increasing homeomorphic self-mappings of R. We define a harmonic extension of such functions to the upper halfplane by means of the Poisson integral. Our main results give some sufficient conditions for quasiconformality of the extension.
LA - eng
KW - Harmonic mappings; Poisson integral; quasiconformal mappings; harmonic mappings
UR - http://eudml.org/doc/268030
ER -

References

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  1. Ahlfors, L. V., Lectures on Quasiconformal Mappings, Van Nostrand Mathematical Studies, D. Van Nostrand, Princeton, 1966. 
  2. Kalaj, D., Pavlović, M., Boundary correspondence under quasiconformal harmonic diffeomorphisms of a half-plane, Ann. Acad. Sci. Fenn. Ser. A. I. Math. 30 (2005), 159-165. Zbl1071.30016
  3. Lehto, O., Virtanen, K. I., Quasiconformal Mappings in the Plane, 2nd ed., Grundlehren der matematischen Wissenschaften 126, Springer-Verlag, Berlin, 1973. Zbl0267.30016
  4. Pearson, K., Tables of the Incomplete Beta-Function, Cambridge Univ. Press, Cambridge, 1934. Zbl0008.30403

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