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Proceedings of the American Mathematical Society

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Distance and volume decreasing theorems for quasiconformal mappings


Author: Nicholas C. Petridis
Journal: Proc. Amer. Math. Soc. 83 (1981), 93-98
MSC: Primary 32H25; Secondary 30C60, 53C20
DOI: https://doi.org/10.1090/S0002-9939-1981-0619990-5
MathSciNet review: 619990
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Abstract: The method used by the author in deriving a Picard type theorem for quasiconformal mappings [Proc.. Amer. Math. Soc. 61 (1976), 265-27], improved by a proposition of S.-T. Yau [Amer. J. Math. 100 (1978), 197-203] is employed here to extend the Schwarz-Ahlfors lemma to harmonic quasiconformal mappings. The target space is not necessarily hyperbolic, not even negatively curved.


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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1981-0619990-5
Keywords: Quasiconformal mappings, harmonic mappings, scalar curvature, Schwarz-Ahlfors lemma
Article copyright: © Copyright 1981 American Mathematical Society