J. Heinonen, THE DIAMETER CONJECTURE FOR QUASI-CONFORMAL MAPS IS TRUE IN-SPACE, Proceedings of the American Mathematical Society, 123(6), 1995, pp. 1709-1718
The diameter conjecture for quasiconformal maps is a natural generaliz
ation of the Hayman-Wu theorem on level sets of a univalent function.
Astala, Fernandez, and Rohde recently disproved this conjecture in the
plane. Here we show it is true in space.