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Proceedings of the American Mathematical Society

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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$.

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

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