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



Conformal mappings and the distortion of moduli of rectangles

Author: Bruce Palka
Journal: Proc. Amer. Math. Soc. 50 (1975), 155-161
MSC: Primary 30A60
MathSciNet review: 0369693
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Abstract: In this paper it is shown that for an orientation-preserving homeomorphism $ f$ between domains $ D$ and $ D'$ in $ {\mathbf{\bar C}}$ to be conformal it is necessary and sufficient that there is an $ a > 1$ such that $ \bmod f(Q) = \bmod Q$ for each square $ Q$ in $ D$ and for each oriented rectangle $ Q$ in $ D$ with $ \bmod Q = a$.

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

  • [1] Cabiria Andreian Cazacu, Sur les inégalités de Rengel et la définition géométrique des représentations quasi-conformes, Rev. Roumaine Math. Pures Appl. 9 (1964), 141–155 (French). MR 0180673
  • [2] F. W. Gehring, The definitions and exceptional sets for quasiconformal mappings, Ann. Acad. Sci. Fenn. Ser. A I No. 281 (1960), 28. MR 0124488
  • [3] F. W. Gehring and Jussi Väisälä, On the geometric defintion for quasiconformal mappings, Comment. Math. Helv. 36 (1961), 19–32. MR 0140684,
  • [4] J. A. Kelingos, Contributions to the theory of quasiconformal mappings, Thesis, University of Michigan, Ann Arbor, Mich., 1963.
  • [5] O. Lehto and K. I. Virtanen, Quasikonforme Abbildungen, Die Grundlehren der mathematischen Wissenschaften in Einzeldarstellungen mit besonderer Berücksichtigung der Anwendungsgebiete, Band, Springer-Verlag, Berlin-New York, 1965 (German). MR 0188434
  • [6] O. Teichmüller, Untersuchungen über konforme und quasikonforme Abbildung, Deutsche Math. 3 (1938), 621-678.

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Keywords: Conformal mapping, quasiconformal mapping, modulus of a quadrilateral
Article copyright: © Copyright 1975 American Mathematical Society

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