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Transactions of the American Mathematical Society

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Sharp distortion theorems for quasiconformal mappings


Authors: G. D. Anderson, M. K. Vamanamurthy and M. Vuorinen
Journal: Trans. Amer. Math. Soc. 305 (1988), 95-111
MSC: Primary 30C60; Secondary 30C75
DOI: https://doi.org/10.1090/S0002-9947-1988-0920148-1
MathSciNet review: 920148
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Abstract: Continuing their earlier work on distortion theory, the authors prove some dimension-free distortion theorems for $ K$-quasiconformal mappings in $ {R^n}$. For example, one of the present results is the following sharp variant of the Schwarz lemma: If $ f$ is a $ K$-quasiconformal self-mapping of the unit ball $ {B^n}$, $ n \geqslant 2$, with $ f(0) = 0$, then $ {4^{1 - {K^2}}}\vert x{\vert^K} \leqslant \vert f(x)\vert \leqslant {4^{1 - 1/{K^2}}}\vert x{\vert^{1/K}}$ for all $ x$ in $ {B^n}$.


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DOI: https://doi.org/10.1090/S0002-9947-1988-0920148-1
Article copyright: © Copyright 1988 American Mathematical Society

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