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The diameter conjecture for quasiconformal maps is true in space

Author: Juha Heinonen
Journal: Proc. Amer. Math. Soc. 123 (1995), 1709-1718
MSC: Primary 30C65
MathSciNet review: 1234626
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Abstract: The diameter conjecture for quasiconformal maps is a natural generalization of the Hayman-Wu theorem on level sets of a univalent function. Astala, Fernández, and Rohde recently disproved this conjecture in the plane. Here we show it is true in space.

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