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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

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

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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On the area distortion by quasiconformal mappings
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by A. Erëmenko and D. H. Hamilton PDF
Proc. Amer. Math. Soc. 123 (1995), 2793-2797 Request permission

Abstract:

We give the sharp constants in the area distortion inequality for quasiconformal mappings in the plane.
References
  • Kari Astala, Distortion of area and dimension under quasiconformal mappings in the plane, Proc. Nat. Acad. Sci. U.S.A. 90 (1993), no. 24, 11958–11959. MR 1251715, DOI 10.1073/pnas.90.24.11958
  • A. Eremenko, On Astala’s proof of the area distortion theorem for quasiconformal mappings, preprint, December 1992.
  • F. W. Gehring and E. Reich, Area distortion under quasiconformal mappings, Ann. Acad. Sci. Fenn. Ser. A I No. 388 (1966), 15. MR 0201635
  • D. H. Hamilton, Area distortion of quasiconformal mappings, Handbook of complex analysis: geometric function theory, Vol. 1, North-Holland, Amsterdam, 2002, pp. 147–160. MR 1966192, DOI 10.1016/S1874-5709(02)80007-5
  • O. Lehto and K. I. Virtanen, Quasiconformal mappings in the plane, 2nd ed., Die Grundlehren der mathematischen Wissenschaften, Band 126, Springer-Verlag, New York-Heidelberg, 1973. Translated from the German by K. W. Lucas. MR 0344463, DOI 10.1007/978-3-642-65513-5
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Additional Information
  • © Copyright 1995 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 123 (1995), 2793-2797
  • MSC: Primary 30C62
  • DOI: https://doi.org/10.1090/S0002-9939-1995-1283548-8
  • MathSciNet review: 1283548