The diameter conjecture for quasiconformal maps is true in space

Heinonen, Juha

doi:10.1090/S0002-9939-1995-1234626-0

The diameter conjecture for quasiconformal maps is true in space
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Proc. Amer. Math. Soc. 123 (1995), 1709-1718 Request permission

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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