On the Hayman-Wu theorem for quasilines

Abstract

For a function ω, we establish a condition sufficient for the sum ∑_i, ω(diam φ(L _i )) to be finite for any quasiconformal curve L _i , simply connected domain Ω, and a function φ which conformally and univalently maps this domain onto the unit disk. Here, L _i denote the components of Ω∩L